AP Yi works, and doesn't even require 'near perfect' play, though he isn't anywhere near as strong as he used to be.
The 4.0 AP scaling heal on meditate with the free 300 Armor/MR allowed him to tank basically any amount of damage from any champion without a hard CC readily available, which allowed him to be a very powerful control bot laner. The strategy was (and presumably still is) to sit in the bush until alpha strike was up, then alpha strike a minion when the enemy champion is also in range, killing the minions and damaging the champion, then running back into the bush. Since it's a heal, it scales on cdr and AP, instead of on cdr, AP, and Mpen, like a damaging ability would, so yi would benefit most from rushing to a deathcap (now witchcap) and 40% cdr.
Yi's major weakness as a bot laner was that if the enemy had a reliable hard CC to interrupt your meditate, or you got ganked by a champion with hard CC too often, there was no response possible, making every lane pretty binary. That was compounded with the fact that control bot is rarely better than an aggressive bot lane that manages to kill the opponent.
His ult is actually best used bot to run away from ganks. Using it, you can outrun basically anyone, with any build and any speed steroid. If you are feeling extra agressive, the cooldown reset from getting a kill while Highlander is active also resets the cooldown on Deathfire Grasp, and DFG can be cast while you are untargetable due to alpha strike, allowing chaining of kills once you hit a full, lategame build. The difficulty is that it is very hard to do that before lategame happens and you have 500+ AP, full CDR, DFG, Void Staff, etc.