Tips for beating Buddy Buckets?

Well, while my measly 1550 rating doesn't qualify me as a chess coach, I think it's clear enough that "20. Bxf6" was a major error that became decisive for the game's outcome. Not only did you exchange a bishop for a pawn instead of pulling back the bishop and exchange it for your opponent's strong bishop aimed at the f2 square, it opened up for the following attack on your king, too.
On the positive side, bots on this level can be beaten even if you make several minor errors, so just try again.
Oh, and you asked for tips for the future, too.
Erm, while it's generally smart to castle quickly for players on your rating level, the bots "wayward queen" can be used to your advantage if you can make it a target in the opening.
Naturally, this means playing more aggressive opening lines against the bot. The following is a theoretical line based on the one game that I can see that you played against the bot. While this line doesn't involve chasing the queen (but always look out for this opportunity), it takes advantage of how the queen gave up its defense of the central pawn:: 1. e4 e5 2. Nf3 Qf6 3. Bc4 Qh6 4. Nxe5 [the likely bot move] Qg5 5. Qf3 ...
With this line, you would have won a pawn in the opening and you would have gotten a much better developement than the bot (the threat of checkmate on the f6 square by your qeen means that the bot cannot capture your horse on the e5 square).