The story more or less has at its concept nothing particularly groundbreaking. I'm thinking urban fantasy, emphasis fantasy here, where magic is commonplace and many modern things don't exist using technology (but might exist using magic, though some may not), but many other modern things do. Things like cars, cell phones, the internet and the like are definitely in the setting, as is electricity. Other than that, not exactly sure.
But anyway. Central point here is that it's mostly a fantasy world. As a result, dragons are...a big thing. Dragons are the creature with the greatest natural storage of magical energy: their vast magical reservoirs dwarf a comparative human's level, but this comes at a small price: they lack the efficiency humans have. The dragon's natural form is difficult to cast advanced magic in. Basics like flight and fire come easily enough, but in draconic form, they lack the finesse necessary to manipulate magic with ease. (You can make magic do anything with your mind, but it's much harder and less efficient than using your limbs to aide and guide the magic. Because dragons aren't exactly the most nimble of creatures, their magic is therefore less efficient.)
Now, dragons can shapeshift using magic, and in a shapeshifted form, they maintain much of their draconic qualities. In fact, a dragon in human form is actually more efficient a mage than a natural human. However, there's a tradeoff involved: shapeshifting is not easy to do. It robs them of the majority of their magical reserves, because maintaining human form is basically a constant, neverending strain on their powers. So, when in human form, a dragon has access to less magic than a human would.
In short, when as a dragon they have far more magic than a human but far less control; when shapeshifted to be a human, they have a little less magic than a human but at least have some greater control than your typical human mage would.
Somewhere along the line, though, something happened: dragons developed the ability to bond with humans. Now, this isn't "dragon riders". A bonded human may ride a dragon, but over half won't. This isn't "dragon masters". Bonds are never master-pet. Either way. (Not dragon in control, or human in control.) Always, it's a deeper connection between the two which places them on an equal level, where they are both individuals, who just so happen to have linked together.
Said bonds can be any number of relationships: simple partnerships, a friendship, with the bonded being like siblings, with it being a parent-child dynamic, it could be student-teacher, or even on rare occasions, lovers. (Among other bond types.)
These bonds aren't set in stone, and aren't even labeled. Bonds are bonds. When they happen, it means you have a lifelong companion, and that means that they are someone you will get along with more than you won't (bad bonds cannot happen), but what the bond is, that's up to the chemistry between the individuals. It can start as one type, and develop into another. From student/teacher to partnership to friendship to lover, for instance. But it doesn't need to be any concrete type. Bonding just...simply is. It happens when it happens, and then they get to decide what that means.
And they have a long time to do so, because bonds are life-long. There's no way to break a bond, though there wouldn't ever be a need to. (While you might not always get along with the one you're bonded to--everyone has disagreements--the bond represents your potential to have something special, something magical, together, something that you two together would do well in.)
And the main reason for this bond? The massive level of synergy it provides. Dragons, when bonded to a human, have the efficiency of one, even in their draconic form. (So long as the bonded human is close enough, at least.) The human in question gets the obvious magical boost, which is something that can come quite in handy.
And this even allows for a dragon to shapeshift while maintaining the vast majority of their magical strength, though because of them having the increased efficiency by virtue of the bond, taking human form is something of a personal preference. (Some dragons really like the form of the human body.)
With this set, obviously, half-dragons can and will and have been born before. They basically have the benefits of a bond without being bonded: they have a mostly-human form which offers them fully human efficiency, with the majority of their magic; they can shapeshift into a mostly-dragon form which maintains most of their human efficiency, while allowing for the rest of their magic to come out.
Most half-dragons prefer their human form. (Also, the child of a half-dragon will be the race of the other parent: a dragon with a half-dragon will have a full-dragon child; a human with a half-dragon will have a full-human child; a half-dragon with a half dragon will have a half-dragon child.)
Which brings us to our protagonist. She, like most half-dragons, prefers her human form. What makes her unusual is that most half-dragons don't form a bond. It's certainly heard of, especially to humans. The half-dragon bonds to a human. She's an oddity, though, in that she's one of only a few half-dragons ever to have bonded with a full dragon.
In this case, a more sisterly bond, in that the two were raised close together from childhood, and know each other well and treat each other as if sisters, in spite of them having no blood relation. But later down in the story, something happens which is the first ever known instance: she also bonds to a human.
Because a half-dragon is half of each, they can bond to a dragon thanks to their human heritage, and can bond to a human thanks to their dragon heritage. Nobody ever thought it was possible to do both, even though there was nothing logically stopping it from being possible. It just never crossed anyone's mind as being something that could happen, until...it did, to her.
The polybond in this case doubles as polyamory, in that her dragon-bond (basically sister) loves the same human she falls in love with (of course, there's lots of fun involved in this, in that she originally assumes the feelings are from the bond with her dragon-bond, until it's made explicit "No, you idiot, that's just you" because while bonding does cause a lot to be shared, that level of fundamental deep emotional transference is simply not how things work), and he loves them both.
That's about as far as I got story-wise, though I did also create the symbols which would display on a human-bonded-to-a-dragon, and a dragon-bonded-to-a-human. (Our protagonist eventually ends up with both, one on each arm in this particular case.)
All this, for a sketch I haven't even made yet.
But I'm looking forward to it.