Green’s Dictionary of Slang

BB’s n.

[abbr. SE big brains]

(US black campus) a clever person, a teacher.

[US]M.H. Boulware Jive and Sl. n.p.: BB’s ... Big brains, a teacher.
[US]T. Philbin Under Cover 92: Good old boys with egos the size of BBs who want to prove how tough they are.