I did a nude 5K once, it actually wasn't bad in that department. I can imagine that nude bike riding is along those lines: harder to imagine than it actually is.

After all, mammals have been running long before underwear was invented.

Edit: I just sat on my bicycle in my garage, and I don't see it being an issue. Try it out, although research nude etiquette, laws, and places to go first :-)

You can start here: https://www.aanr.com/aanr_articles/the-history-of-nudism/