This is my first non-loss against a player rated as high as my opponent was. The game turned out to be a draw, but I think I had some decent winning chances at certain points in the game. Any feedback would be appreciated.
You hold no advantage in the final position, a draw was correct.
(The Bishop is unlikely to be better than the Knight, the pawns are all on one flank, this negates the Bishop's speed across the board and slightly "powers up" the Knight).
It gets very complicated...but it's possible that the move 27 Ra1 held some promise. The idea is 27... Bxb2 28 Ra7. Then (among other things) Bd5 can prove annoying.