I would assume that this strategy would lose to BMU, maybe +1 Bishop. The amount of deck-thinning you're doing for your opponent sounds extreme.
I would not blindly buy Bishop all the time with $4 or $5. I'd try to keep my deck no more than 20-25% bishop. While it may be fine to have Bishop/Bishop/money/money/money, on the theory that you trash the second Bishop, it's a hell of a lot less all right to have Bishop/Bishop/Bishop/money/money, since then the third Bishop is entirely "dead."
I would probably not buy Gold with $8 available unless I got a really early $8 (and I kind of struggle to see how I even could get that). With Bishop thinning your deck constantly, I'd expect that my "normal" Gold buys would keep me in pretty good money, so Provinces wouldn't need to be deferred for more money.
I presume that I would trash coin over green in cases where the game was very close to ending and trashing my coin would not cause me to go down a tier of green buys this turn, and where trashing the coin nets me more VP than trashing the green. Example: Hand is Gold/Silver/Copper/Bishop/Duchy. I can only buy a Duchy at best. I can still buy the Duchy if I trash my Copper. If I trash my Duchy and buy a Duchy, I get net +3 VP, whereas if I trash my Copper and buy a Duchy, I get net +4 VP.
I note that all of this is pure off-the-top-of-my-head, no real play experience, so take it with a huge bag of salt.