The book was about people from the entertainment industry in Hollywood (actors, writers, producers etc) who start disappearing. Turns out they are somehow being transported to some alternate universe or past time period that’s medieval like. There is some reason they don’t want people from there to know (I can’t remember why) so they start going around in a traveling wagon putting on a Shakespeare play – Hamlet I think, and advertising a miracle cure all – I think it was aspirin. The idea is people from our world/time period would recognize both but the people from there wouldn’t!
Maybe ‘Gone for Good’ by Mark Childress?