Dry Cleaning cotton shirts won't really get them clean. Most of the stains and daily grime and sweat (etc.) on the shirt will be water based and dry cleaning just doesn't clean water based stains.
My Suggestion:
- Buy enough shirts for 2 weeks
- Use a laundry service that returns the shirts to you.
- Enjoy freshly laundered, crisp shirts on your back.
This advice will also stop your shirts smelling like they've been worn for a few days too.
-- DrClean