It isn't the ability to do efficient bit operations that is a strength of C - it is the ability to easily and succinctly do whatever you want to the bits in memory. Arbitrary pointer/memory operations help greatly in writing things like memory managers, device drivers, and all of the other wonderful parts the make up the guts of an OS.

edit: Added the text "easily and succinctly" as a qualifier on doing things to bits in response to stcredzero's comment. It isn't that C is the only language to allow it, it is that C allows one to do it without obscuring your intent. C# handles this quite well with unsafe blocks, Java not so much.