Thank you everyone for your responses. I hope I didn't bias the poll, but it looks overwhelmingly in favor of my assumption, which was option A.
The controversy in my game surprised me because I do have fairly experienced players, so I guess we are just the victim of an incorrect local custom here.
I do want to give
@inca911 some credit for an outside the box answer C, that did get a few votes.
The correct procedure for a bomb pot is a little more complicated. As you are dealing the flop immediately after the last player receives the last card (i.e., customary with bomb pots) you should not burn the flop at all since the deck has not sat with the top card exposed. The reason for a burn is to remove a "stale" top card that has been sitting visibly exposed on the deck. If the deck has not sat exposed, a burn should not be performed to ensure maximum consistency to the true intent of a burn.
The correct answer for a bomb pot is C) 0 (flop), 1 (turn), 1 (river).
Technically, I am executing the most consistent procedure of conducting a burn only when the deck has sat idle and exposed. It’s not about the streets, it about the idleness. Else you would burn once for the Turn and again for the River in IMPLOCEAN, prior to burning the Ocean. I'm not going to die on that hill trying to win that battle, especially with Dave!
And I do agree, given the main reason for burning is to follow a betting round where the back of the top card sits exposed. A good secondary feature is that it slows down the game just enough to allow players to catch a dealer that may be about to deal prematurely. But again, that wouldn't apply to a bomb pot with no preflop action. (A proper dealer slows this down even one step further by rapping the table before burning and turning.)
Good procedure also means separating the burn cards so they can be used to track the hand and solve questions as to whether or not the "burn" is down." Which is why I am compelled by
@BGinGA 's point.
1 burn card per street, regardless. I see no valid reason to alter standard dealing procedure just because of a different betting structure or the number of dealt board cards per street.
Imo, 'procedural consistency = less confusion' trumps all other reasoning.
I do think reduced confusion is a good enough reason to keep the burns the same in a hold'em game, even if not "technically necessary" in a bomb pot as
@inca911 pointed out above.
If the procedure of omitting the burn card for bomb pots became a standard, then dealers used to there being 1 burn down before the flop, 2 burns down on the turn, and 3 on the river have to mentally make that change for a bomb pot even if the mechanics of the deal are the same. That might cause confusion, even if momentary. That's significant enough for me to agree with keeping the procedure the same.
Also it would not be "technically necessary" to burn after an all in (except for the current card on the top of the stub), but I don't think anyone would argue for changing the dealing procedure in that instance either.
So now this thread can officially be a debate between "A" and "C", and one person voted "B" but didn't say why.
Thank you everyone for your feedback.