Why you should never resign in bullet
Anything can happen in bullet chess. The clock times are always so low that no matter how objectively worse 1 side is, it still much of the time comes down to which side has more time. With this in mind, I argue that there is no reason to resign in bullet games no matter what. I will show you a game in which I never tried timeburners, my opponent still had a minute by move 25, but he did not manage his time well, and somehow managed to lose. Now first I want to make something clear: If you are on the losing side of a game like this in any time control other than bullet or blitz, but especially bullet, then you should resign because the etiquette calls for it. In other worlds, you should resign unless your opponent doesn't have enough time to deliver checkmate. The strategy black used to win this game is acceptable in bullet because the clock times are so low that there is virtually no losing–>resign etiquette. So I do not play with this strategy under standard time controls and do not recommend it for anybody.
Again, my argument is that one need not resign in bullet no matter what, because if black were able to win the game shown above, then anything can happen in bullet, so resigning is always too early in bullet, except for the final position of the game, where resigning makes sense.