Most of the bidets--even super cheap basic ones--have a mode where they can flow water over the nozzle to clean it off. Regardless: if you shoot clean water through the nozzle you are momentarily maybe going to send dirty water at your already dirty body--so, no biggie--but then the water is going to run out of stuff to carry with it, and help clean you.

What water? It depends on what model you get.

On the cheaper models, the nozzle is always there, so yeah it'll be another surface that needs to be cleaned.

On the more expensive models, the nozzle is in a separate chamber until it is being utilized, and has a separate mechanism for spraying / cleaning itself. That makes it a lot less of a cleaning burden.

Toto washlets have a function to automatically clean the wand/nozzel. I expect others do as well.