We are doing the same connection albeit from GLA later in the afternoon at the beginning of June and also staying at the same hotel, we have chosen National Express and allowed a 50 minute gap to collect luggage. It was around £50 one way for 2 of us and for me it is the an easy transfer, though as Bison rave says a meet and greet taxi will also work well. Hope all the feedback helps you choose what works best for you