Yes, but you need to sign up for it when you first check-in. It services all cruise lines, so you may stop at other ships before you reach Regent. Opted for the shuttle first time I stayed. Did Uber second time I stayed. Unfortunately we did not have a good Uber driver (couldn't find our hotel, then got lost finding Terminal J so we brought up Google Maps and directed him, limited English). Would probably use Uber next time and hope for a better outcome!
Hotel is a Hampton Inn, so you know what to expect. Pleasant people, good breakfast.