I think Trist just starts out too slow. She needs multiple levels in both E and Q to take down turrets effectively.
I would assume a lot of the strategy comes down to figuring out which bots to go against. You want someone with no wave clear at all, and some of that might just come down to figuring out which bots don't use their skills to clear minions at all.
I'm assuming you want to find a champ with high base stats then just stack AS as long as you can stack the bots to be no threat to you.
Is there some cheesy strat where you can get a free recall to shave off 10s by taking Revive as a Summoner Spell?
The challenge isn't really interesting enough to put any thought into, in the end it comes down to execution.
For your champion you need waveclear, a steroid and most likely be ranged. For the bots you would want them to not have waveclear, probably be melee and not just have a kit a bot can't use properly.
So for champs that are the fastest it's prob gonna be Jinx or Trist. Azir scales to slowly, Malzahar could be interesting with his voidlings.
Elise with spiderlings(not sure how they work on tower) or Yorick could be interesting as well.
Summoners will be TP + Ignite or Clarity, and Runes Attackspeed or CDR for the most part.
Sometime around last year when intermedeate bots came out I tried to see if I could 1v5. IIRC I did it with old tristana (didn't have a good time tho). I just wave cleared until death timers were long enough so that I could get inhibs after a penta. Was very hard to win on an AP champ for me.
New tristana is good vs towers, but I thought she would run into mana problems. All depends how many times you need to back.