If my membership site becomes popular and BlueHost decides it's not in their interest to keep hosting, is it easy to transfer all of the files and member data to a new server?
I recommend you to have a look to http://www.mddhosting.com/132 - they are familiar with aMember and I've heard no bad things about them. As I know, skippybosco represents this hosting in our forum. Regarding the transfer itself: http://manual.amember.com/FAQ#Move_aMember_to_new_host