To be honest, and I am happy someone is thinking about my favorite forgotten yordle, I don't think this is what she needs.
Mostly on a basis of its just numbers, where what she needs is her kit in itself to change a little bit. If I had to mess with the numbers, it would be with AP scaling on E so it increases with level like it does with AD and ends up higher over all, because AP Trist is fun.
A lot of Tristana's kit is unique, while just as much is mundane. EG her passive, W, & E are unique, while Q & R are kind of mundane. If I had to change anything really, it would be to Q or R.
Q: Rapid fire
Increases attack speed, allowing for quick E stacking early and strong bursts of strength at higher levels, which reminds me slightly of another champion, Jayce cannon W. Kinda sad though nowadays that a lot of champions have better steroids, like Xayah W, Draven WQ, and Twitch Q. Tristana's steroid is BLAND, sure its strong but it's so bland it feels kind of dumb and un-impactful to cast, despite how strong of a skill it really is.
R: Buster shot
Massive cannonball, hits one champ for big damage but can knock back multiple units in a small range. Range and knock back scale with level. Mini Lee sin kick but ranged. Also it knocks back from WHERE IT WAS INITIALLY CASTS, so if you cast and then flash behind them it will still knock them away from your initial position. Most of the time is a self peeling tool or finishing move, hardly ever will you just knock back someone for extra damage because they can just get away + half the time you fail the finishing move and just push them to safety. I seriously want an indicator for this.
Some things I would be interested in for changes:
Q needs to have the same goals in mind: Strong periods of power + Stack E quickly. She is kind of like Jinx in identity, demolition master(hence her love for explosions) This may be a tad overpowered, Reduce duration, remove attack speed bonus(or increase it for only the first few shots), but every shot proc E passive. E passive now stacks E active. Essentially a double shot. It may weaken her late game a little bit, but honestly should make her early game a little more bearable. E passive damage may have to be scaled down. Also please please please, make the indication range of E passive explosion more visible. CD may have to be increased at early levels but depending on how it interacts late game, should scale down lower.
R should feel more like a boom skill, not just a fuck-off-I-have-a-big-cannon. Buster shot doesn't even make an explosion, just a solid lump of steal smashing into someones face breaking into little molten pieces. Make it explode. Enemies in the range are knocked AWAY from the explosion and take damage(Base damage reduced, AP scaling remains), Targeted enemy still is knocked back.
TBH I am biased, because I like AP Tristana as much as AD Tristana.(Side thought, change more AP scalings into E and remove from W)