I am looking to book some celebrity comics and athletes a show for my podcast. Is there an easier way than contacting a bunch of managers? What is an idea of cost for one show

I have a celebrity client who would fit that genre who may be interested

Bookings for podcasts are done through the publicist. If the celeb, doesn't have a publicist then you would get in touch with the manager.

Interviews are typically done for free, and publicists usually evaluate podcasts by their audience size, demographic, and the type of interview. Though most interviews are done for free, there are cases where outlets pay celebrities' to appear on their show, but this isn't typical.

To invite celebrities to your podcast, you will need to contact their publicists. I'm afraid there is no easier way as inquiries like this will have to go through celebrity representatives (In your case, their publicists). The good news is a single publicist usually represents multiple celebrities. So the publicist may be able to suggest other celebrities that are suitable for your podcast.

Interviews on podcasts are basically a promotional tool for the celebrity so they are usually done for free.