I use a sort of wave, raising my hand but with no movement in it (so not a 'Hey buddy' or 'I need help' side to side movement).... it works on my bicycle, on my motorcycle, and while driving a vehicle. It's got somewhat of a dual purpose: acknowledgement that I did something wrong, and/or 'thanks for letting me in' gratitude gesture.
The motorcycle I find a very odd case of this. It's 95% not me giving the gesture, but receiving it after being cut off, not seen, turned in front of, etc. People are in general not interested in showing any rage and are quick to apologize when I'm on one, even if I'm not wearing the armored jacket and helmet. I don't get even half this respect in vehicles or bicycles.
That was a side note that I've found interesting, but the point is that it's the same gesture I seem to get from many other people. There's no side/side or waving motion, just a hand up, fingers together, "Thanks/Sorry".