I've been practicing a ton of music in the last year because I would like to play some music at local coffee shops/restaurants.

I was wondering how playing copyrighted music worked? Some things are in the public domain. As far as I can tell, Gershwin, Zez Confrey, most classical piano pieces etc are in the public domain (because they are old af), so playing them is super easy

I would like to play some music from Studio Ghibli and maybe some piano solos by William Bolcom copyright 1971.

Is there a way to pay to get permission to play these sorts of pieces? Who would you even ask? Can you get a "license" of sorts to play copyrighted music?

Thank you in advance.