Just stay ahead on the clock and you'll be just fine; yes, do not, ever, under any circumstances resign. I say just the opposite; do not ever exchange pieces, and go for the time win.
how to win at 1 minute games even if you're not that good at chess

1play some troll opening, 2Avoid long moves(they waste time)3 ignore all threats save mating ones,4Check always when you can 5use your king as much as you can,King attacks are very effective in bullet.6 be brave

http://www.chess.com/livechess/game?id=890508520
check this one, dead to rights and I sack a rook for one last check and it surprises him so much his 1.4 expires for the cheap time win. His response: Genius!!
NEVER RESIGN!!

this advice is so bad its no wonder that you're rated below the average.
novelties are x1000 stronger in bullet than in any other time control. you have worked out the line off the board while your opponent has nearly no time to think of any refutation. playing a predictable opening is bad.
1 minute is actually a long time to think about knowing what to play. if you don't think at all you will find yourself checkmated in less than 30 moves.
if you are up on time, don't exchange pieces. if you are down on time, exchance pieces.
perpetual check works in any time control, that pretty much means nothing.
Use a touch screen app and use both fingers for each side of the board while everyone else is floundering around with a mouse, you'll be 2000+ with no problem.

https://youtu.be/a_vm5aXip_U The Speed Kicks In - 1 Min Bullet: Addicted to Speed, Chess Fun v Super Bot.
i made this up on the spot, correct me