Monster Draw played passively on flop

[RatFink]

Bet the flop.

Yes the BB can raise and cut down field, or he can call, or he can pass out drunk. You don't know, so lead and work from there.

If it gets raised and ends up HU, put in a 3-bet and hope he caps. Lets you check when you miss the turn, and check-raise when you don't.

These situations don't occur often enough, so spew your heart out on the flop.

Edit: p.s. as you described the table, you should have expected BB to check and CO to bet so you'd be facing the field with a 2 bet by going for a check-raise. Makes a lead bet even more betterer.