From the get-go, I basically said they were limited in their powers to what they have available, they just get really, really creative with their usage, from popular culture (e.g. watching Avatar gives great ideas for fire/ice/water/energy/air/earth users) to each other to scientific theories they interpret as convenient to metaphors to literal wording exploitation to watching each other and being inspired by what they see. Not to mention, plain rule of cool.
So on that note, it would be possible for every element to develop their own method of teleporting, even if Hannah is the only elemental rider shown (well, except Whitney) who has that capacity. They just have to find a different way to go about it, working through the process of their element.
For Fire, I haven't actually developed a method for teleportation, but I imagine such a method should exist. Presumably, because I haven't thought of it and I'm generally fairly creative with this sort of subject, it'd be the hardest to do, but this is one reason that my eventual hope is that other people will set stories in the Rubyverse: so that they can go nuts and be creative as they like, with this being one thing that I'd look forward to them seeing a solution for.
Ice, however, is the hardest to master that I have actually thought about. This one I've actually explained on the blog before: Ice is one of the primary elements covering the subject of time, more specifically covering how to slow time down. Because time is tied to spacetime, this gives a very limited control over spacetime, allowing manipulation over a short distance to warp into a specific location. This is where Whitney earned the moniker "Sky Shinobi" (she originally registered as a professional superhero under her given name, only changing it to Sky Shinobi after she had already earned the title): she would use Ice's innate ability to determine the opportune moment to strike and cause the desired chain reaction, slow time down, and teleport in, usually from above (thus, sky), seemingly out of nowhere, strike, then disappear again, like a ninja...aka, a shinobi.
Water is also hard to master, but it's possible, via the concept of 'Slipstream'. Why can water-users theoretically use the slipstream? Because it's a stream, and streams are covered by water, the same way a sound-wave is a wave. It's extremely difficult to master, however. For a start, first the water user has to even be aware they can control the concept in the first place. Then, they have to somehow work out the mechanics of slipstream, because slipstream is an incredibly-vague concept that is incredibly open to interpretation, so simply knowing about the word isn't enough for them to have control.
Even if they have the imagination and creativity to devise a viable system, they then also have to have incredible technical precision to navigate slipstream with the mastery necessary to make teleportation viable, and even then, they have to have a vast amount of energy at their disposal.
Gary theoretically qualifies for all of this, so he could technically use it, but I have no plans for him using it at this time, especially since slipstream has a limitation: it can only be used for long-distance travel. To travel a short distance, they must first slipstream away to a distant location, and then slipstream back to the desired close location, doubling the energy requirement.
Earth is pretty similar to Water, except it uses wormholes. Why do wormholes fall under earth's jurisdiction? Because it's a wormhole, and worms are an inherent part of nature, a sub-section of Earth. Like I said: wordplay is a huge part of the diversity behind what elements can do. Exploiting the exact wording of concepts is how basically every higher-level technique is created using the elements, with a few exceptions that rely more on metaphors.
Anyway, the rules of wormhole travel are that it's easiest to make a mid-ranged transit. This is because opening up a short-ranged wormhole takes a lot of control and energy, and opening up a long-distance wormhole takes a ton of energy maintained over the whole time it takes. Like Gary, Sally does have the theoretical capacity to learn this method, but I have no plans for her actually using it. Maybe she doesn't learn it, maybe she does and simply never uses it, but I don't have her ever teleporting by her own power as of this time, and I don't intend to force it in.
I haven't quite worked out the specifics here, but I imagine that Light works a lot like the transporters from Star Trek do: converting matter into energy, transferring the energy to somewhere else within the directional limitations, and then converting the energy back into matter. It's easier to master than the above, especially given how well-known the concept is, but I imagine there are still some difficulties, namely, in figuring out the connection between Light and energy conversion in the first place. (It's not an energy technique, because energy mostly covers...well, energy, not matter, though there is a little bit of matter in that element.)
Speaking of Energy...Energy, as of right now, doesn't technically have teleportation. I imagine it could have a method (I thought 'hyperspace' might be a viable fit for the Energy element, but never worked out the details there), but it'd be largely redundant. Why? Simple: because energy-users don't need a teleportation technique.
Now...my knowledge of DC canon is a bit iffy, especially since they are constantly and consistently changing what said canon actually is. But I believe that, at least at some point, The Flash could run around the entire world in a little bit over seven seconds flat. Think about the implications there for a bit. In seven seconds, he can make a round trip and end up exactly in the spot he started in. That means, in seven seconds or less, he could be anywhere in the world.
Of course. He achieves this by running really, really fast. So it's not true teleportation. And there is time passing, so it's not truly instantaneous. But it is, effectively, teleportation. It is being in one location one moment, and a different location the next, faster than humanly possible.
And this is Vili's preferred combat tactic. There's a reason she's theoretically one of the strongest elemental riders: combining the superpowers of The Flash and Magneto (and then adding in some extra that not even they can do) produces a superhero who can do a ton of things. So while they might not have teleportation, it's because they don't need it, their innate ability to move really, really fast is more than enough to compensate. (Technically, an Ice user of sufficient power can slow time down as to allow for a similar trick, even without warping space, because slowing time down is easier than manipulating spacetime, but they must be able to slow time down everywhere, for an extended period of time, which takes a VAST amount of energy, but is not impossible.)
As such, energy users are much higher up the chain of ease for teleportation than others, even though they don't actually use teleportation, simply because they mimic the effects of teleportation better than most actual teleporters do.
They are, however, beaten by darkness users, who land in second in terms of ease. I've talked about this a bit before, but basically, darkness users have a myriad of different ways they could teleport. (Okay, so technically, that's true of all the elements: these are the ones I have thought of, and are probably the easiest for the elemental user to master, but just because they're the method I list doesn't mean that other methods don't exist.)
One of the easiest is simply to open up a void, and instantaneously travel from one spot to another using this. Think sort-of like Portal, in that they simply open up a gap, pass through it, and exit through another gap of their creation. This does mean their transportation, similar to Earth and Water, is not instantaneous (they have to step into it), but it's easy to think of (it's not too uncommon in popular culture), it's easy to master, it's quick, it doesn't require much energy, it's probably the most commonly-used method of elemental transportation even though it's not at the top of the teleportation chain.
That honor belongs to Air. Because Air deals with concepts. There are multiple ways someone using Air can teleport, yes, but Air teleportation, at its simplest, can just be the user thinking. Literally, just a thought. "I want to be at *location*." Boom. Instantly, no time delay, no need for movement, and with the capacity to bring others, they transport to that location. And, it also works with people...even if they don't know where that person is! "I want to be where *person* is." They think it, they will it to be, and instantly it is made so.
This is why Hannah is the teleporter of the team. Short-range, long-range, makes no difference. She can go anywhere she pleases, in an instant, without consequence. It uses basically no energy at all, it's so ridiculously easy to do, it happens in an instant, it's safer than most teleportation methods, it's basically the ultimate elemental form of teleportation, and among methods of teleportation is still one of the top methods. (I'm not sure it's the top method. There might be a non-elemental method which trumps it. Maybe more than one. But it's among the top methods.)
She can carry momentum, or she can stop dead in her tracks. It is, literally, thinking of a situation to be in, and then going into that situation. Falling at terminal velocity? (Well, that's not a problem for an air user, anyway.) Teleport, and she can be at a dead stop on the ground. (This is unique to air: energy has to stop momentum. Darkness, earth, and water require momentum. Light maintains whatever state the person was in, though it may reduce momentum by virtue of the transfer. Even ice creates momentum!)
Vice-versa works too! She can be at a dead stop, and teleport in motion. There's limits to how fast said motion can be (as fast as they are capable of naturally moving, which for an air user would probably be around 250 MPH: very, very fast, but fairly low on the superhuman scale all things considered), and said motion is only a temporary speed (they lose momentum rapidly), but they can do it all the same.
Basically, it's not at all unfair to say that while other elements can teleport, air is the element best suited for teleportation. And this is why Hannah is the first we see using it, and the most prominent user of it in Red Hood Rider. She simply does it better. It can be used for literally anything they can think of, though Hannah usually only teleports at the request of another.