Can I invite people to my bridal shower if I'm not inviting them to my destination wedding?

You should not invite anyone to your shower who isn't going to be on your wedding guest list. (The exceptions to this policy are very specific, for instance, office bridal showers where co-workers aren't going to be invited to the wedding.) The reason for this is that since showers require that guests bring gifts, it looks grabby to invite people to the lesser party but have them not make the cut for the main event. You can have a little more flexibility if you have a post-elopement or post-destination wedding reception back at home where you invite all of those shower guests, but you have to know that you are going to have the later at-home celebration before you send the shower invitations.