I usually just say "sorry" but you could also say "excuse me" which is very common. In the UK, most people will apologise if they bump into someone else (even if it is not their fault) as there is a code of politeness that most people tend to follow.

"Get out of my way!!" Just joking, ha ha

(I'm a US native speaker). I say something like "excuse me." If it's a bad bump and I think it's my fault, I might say "Oh, I'm terribly sorry, please excuse me."