If decent players play 1 1 bullet, they will not flag unless the connection is bad as you can play 2-3 moves in one second. 2 moves in one second is possible even OTB.
Bullet is of course not as significant as Blitz, which is less significant than Rapid and tournament chess. Still I don't want to judge whether you need 10, 50 or 200 bullet games to get a result that can be compared with one game at tournament time.
But anyways the decisive factor to win in Bullet is chess skill. If you are slightly faster but keep blundering pieces, you might win one lucky game, but never remain on top in a long match.
There are many good chess players, that are weak at Bullet but I have never seen a good Bullet player that was weak at chess.
Just play with 1s increment and mouse speed will play zero role. :)