This is balanced, but the breath weapon has problematic design.
I've input this race into the Detect Balance: a 5e Homebrew Race Guide spreadsheet and come up with a score of 24. It's not a straight conversion, so I'll explain each point.
Ability Score Increases
This is slightly stronger than the original dragonborn by making the +1 a choice instead of fixed. DB rates this at 13 points, the original at 12. Not huge deal, just a small improvement for the little bit of extra flexibility it affords.
Another improvement over the original dragonborn, but also a feature possessed by an official variant, the Draconblood Dragonborn. DB rates this at another 3 points. Still on track to be balanced.
I think this version of the breath weapon is actually significantly weaker in power than the original, and catastrophically weaker at higher levels. For number of uses, you are probably going to be using this breath weapon a little bit more, up to 5 per long rest at 20 con, but only if you are playing a class that uses high constitution anyway. If playing a low constitution character, you do not get your breath weapon very much.
Which brings me to my next point: this breath weapon is pretty underwhelming, especially at higher levels. First, the original breath weapon has scaling damage, up to 5d6 at 16th level for an average of 17.5 damage on a failed save, and 8.75 on a successful one. Further, the original breath weapons were all some sort of area of effect capable of hitting multiple targets. Your evaluation of the original breath weapon as not "very practical for the action economy in battle, the damage is not great, and it has extremely limited use" seems to be pretty far off, and your breath weapon is significantly worse. Your breath weapon hits one target. At 20 constitution, your breath weapon does 1d10+5 for a maximum 15 damage on a hit (at higher levels, less than the average of the original) and zero damage on a miss. This version of the breath weapon is inferior to the original in every conceivable way, except possibly in the very early stages of the game.
The only thing this breath weapon has going for it is that it is a bonus action, which gives it a little bit more utility in that it can be used along with a weapon attack or spell.
I'm giving it 3 points on the DB score, in contrast with the original breath weapon's 6.
This contributes nothing to the score during levels 1-9.
At level 10, we get resistance to falling damage. Falling damage seems pretty situational, and its only applicable from 10th level forward, so I think I'm being generous when I rate this similarly to "one rare resistance", which has a DB score of 2 points. It could probably be 1 point.
At 20th level we get a flying speed. I'm giving this zero points because it contributes nothing for 19 levels.
And finally, the dragonborn gets a medium resistance, which DB gives 3 points.
The original dragonborn has a score of 21, so on paper, this one seems a little bit better. The darkvision and improved ASI make up for the lackluster breath weapon. Its going to be a bit weaker than the Draconblood and Ravenite dragonborn.
Overall this is balanced compared to other dragonborn - slightly better than the original, and weaker than the published variants.
That's on paper. In actual play, I think the breath weapon is going to be a problem. Mechanically, it's usually going to be totally inferior, and flavor wise, it won't feel like breathing fire. It will feel like shooting a heavy cross bow with your mouth a couple times a day. It really feels more like a solution looking for a problem, and the problem you chose doesn't fit the solution you have brought to the table at all.