It comes from this song, http://en.m.wikipedia.org/wiki/All_About_That_Bass, and as far as I know it wasn't a common saying before the song came out. In the song, bass is used to refer to women who are somewhat heavy in the lower half of their bodies. In music, bass refers to the lower notes, so it's a play on words.

Bass can have meanings in 2 contexts. Bass = Lower Vibrations in music,(low notes) as, the opposite of "treble" (higher notes) Or Pronounced differently, Bass (rhyming with "pass") refers to a species of fish.