I've never played with TT or Peasant line, so take my opinion with a little bit of salt.
I think I agree with you - you want to go for an engine here. It's how you do it that I consider wrong - opening Bishop can't be good here (it rarely is). Yes, it trashes and gives you VPs, but at the same time it also speeds up your opponent's deck completely for free (and he is unlucky that your Bishop never connected with his Estate-hand).
Your goal as and engine player vs BM player is pretty simple - trash as fast as you can, establish Lost City - Oracle engine and then smash your opponent with everything you've got: Possession (or multiple Possessions), Bishop VPs (this phase: mid- to end-game is the right time to play Bishops), attacks etc. He may establish a significant Province lead, but if you do all of the above - you'll be able to catch up quickly while his deck will stall. Add Bishop VPs in the mix and you should win comfortably.
In light of that approach - I'd open something like Oracle/Silver to get to $5 and Junk Dealer as soon as possible, start trashing while simultaneously grabbing Lost Cities. On your low-value hand get a Peasant for the +buy. Once you think you'll be thin soon enough, buy Potion and get Possession. Etc. Get Bishop later in the game - but certainly do not open with it.