Ive experienced this as a copteative swimmer, not as a rider, and we called it deck changing. If swimmers can get in and out of racing suits (you know, the kind that are so tight you have groves in your body for half an hour after a 1 min race) it should be rel. easy to get in/out of bike shorts. If you lack a towell big enough anything that you can loop around your waist works.

On the same note - many of the female swimmers did a similar trick by putting a shirt on without putting their arm into the sleeves and stripping down, but I've never personally tried that method.