bishop is not (in general) a good opener. The points you get trashing estates and copper are few, the trashing is slow, and it doesn't help your economy (at best a terminal copper trashing an estate) - all that
plus your opponent benefits from the trashing nearly as much as you.
turn 10 it made a terrible play chooosing a second YW over swindler when it "knew" you had a bane in hand.
turn 11 it trashed its last silver leaving only bandit camp, swindler and two coppers as its only source of $. (the bots do not play remake well.) It should not have been loading up on young witch as you aggressively pursued mercenary - cards like YW or warehouse don't work well with discard attacks.
turn 12 you played swindler before mercenary, which is a mistake since actions you draw with mercenary are drawn dead.
turn 14 it discarded two estates for buys it didn't use instead of remaking them into silver.
turn 15 it trashed YW for duchy - WAY too early for duchies, though it's hard to tell where the piles are at this point. the game lasted 39 (!) turns, so
turn 16 you gained a third mercenary despite the fact that you have very little left to trash.
There's no reason this game should go on 39 turns. No games should go on that long (with few exceptions). Basically, I'd buy villages and some margraves (~3) and some money. Village/smithy type engines can be a bit fussy, but when the draw is margrave, which has the militia effect built-in, you have more time to set it up. Swindler is strong here: spoils -> curse, gold -> farmland, and hamlet -> estate, a bunch of important 5's you can turn into duchy early or, later, mystic, which is generally weak. Fortune teller is an attractive target for your opponent's silvers.
The extension that allows you to set the cards in the kingdom isn't working with YW, so I haven't been able to provide a perfect example of how I'd play this, but here's me playing the kingdom w/o YW:
http://dom.retrobox.eu/?/20130912/log.5075b25251c30da02a09b898.1378995212599.txt I don't think I played optimally here (too many hamlets, not enough silver/swindler), but it's something to compare to. The bot really spammed swindlers to good effect. I picked up the bishop to deal with the junk.