Not so embarrassing due to being drunk at the time, but funny all the same:
Went shopping in Edinburgh about 10 years ago with a mate. Never got past the pub in the bus station. We ended up getting drunk over the course of the afternoon. In those days, traffic was pretty nose to tail all the way out to the Barnton in rush hour. When the money ran out, we got the bus home, sat at the back. Inevitably I began to need the loo. Due to the rush hour traffic progress was very slow. Just before I thought my bladder was about to explode, I had to get off, thinking that beacuse of the traffic jam I'd easily make it back on. I got off, ran up someone's driveway and relieved myself, ah, bliss. But wait, this is taking a while... how can one bladder hold so much fluid?
A good minute later I set off after the bus which was still in view, with my pal waving at me out of the back window, laughing. It took about 2 miles for me to eventually catch up as, every time I drew near to the end of the bus, a gap in traffic appeared and it pulled away again. I had the Grange Hill theme tune playing in my head the whole time. When I finally made it back on, the driver was killing himself laughing as were most of the back of the bus. My pal was in tears.