Before I was old enough to drive, I once was riding with a friend who'd recently gotten food poisoning and who really needed a restroom. He was speeding to get there and, when he got pulled over, told the officer so.

I don't remember the exact words, but after issuing the ticket, the policeman basically said "just pull over and shit on the side of the road if you need to."

If it were me, I'd respond: "Okay, I'll follow you to the nearest public bathroom, but you're still getting the citation."

Someone pulled that on me once, but I saw them pass a few public bathrooms as they cut around a line of cars in traffic to get to the turn lane a bit faster by going down the wrong way of the roadway, so they were obviously lying.

You might have more luck with your lie among lazier/less discerning/dumber cops, it's true.

- Ex-cop