I started off as a drummer. I was putting a band together with some high school friends and had a friend that wanted to play bass but didn't know how. I had some basic knowledge of guitar, so I taught myself the songs we were doing on bass so i could teach him. We played a few gigs but nothing significant. Fast forward a year - I joined a band in college as a drummer, and at the end of the first rehearsal, we started playing around - and I asked if I could try the really cool Rickenbacker the bassist was using. They asked me if I knew how to play bass and I said I knew a few songs. We jammed on a few tunes and they said "we know a couple of other drummers, but no bassists - would you play bass for us instead? (The guy playing bass at the first rehearsal was a guitarist who was doing it as a favor but would much rather be playing guitar).
So, I agreed and learned about 35 songs in a month and a half for our first gig. Haven't looked back and have been a full-time bassist since 1991.
Excellent story.