I believe my introduction to bit shifting is wrapped up somewhere in the quagmire of my first few months of computer science in college. But I actually became pretty comfortable with their usage since the first major piece of software I worked with, vBulletin, made extensive use of bitwise operations in the ACL and options matrices.

It was a super fast, if visually opaque, way of doing the calculations required to facilitate a very complex permission system. I imagine Facebook works in a similar way, if on a somewhat grander scale.