Yes, just drop your luggage off at Bell Services and tell them which Disney Resort you are checking into next. Be sure to keep with you anything you will need before late afternoon, like medicine , swim suit, etc. Because, in most cases you won't get your luggage until late in the day. You have to be in your room in order to have the luggage delivered. They won't deliver to an empty room. Just call once you are in your room, and they will bring it up. Usually this would be no earlier than about 4pm.
If you are going to a park just do as the previous poster advised. If you aren't planning a park visit, just take a Disney bus to a park or to Disney Springs, then use a boat, bus, or Monorail to take you to your new resort in the same way you would use Disney transportation to a restaurant reservation at a Disney resort. Example: You're leaving Pop Century Resort and checking in at The Grand Floridian. Drop off your luggage at Pop Century Bell Services, then hop on a bus to The Magic Kingdom. Instead of entering the park, walk straight to the Grand Floridian Boat Lauch for a quick boat ride direct to your new resort!
