I am a teacher traveling with 22 high school students from NYC

Dear, yes, you can submit their passports and applications. It usually takes 4 working days.

But if you join in a tourist group organized by travel agencies, you can ask the agency to apply group type entry permits for you, which may be cheaper. And the required documents include a notification from a duly authorized travel agent in PRC, a printed application form, passports and photocopies, as well as a recommendation letter issued by the travel agency. It usually takes 5 working days.