I've heard they will do that for a cruise, but not sure if they will do it for DME.
In any case...why bother?? You can just go to the DME checkin counter, with your bags, and get checked in that morning. Your bags will then go on your bus with you...well, underneath the bus. That way you will have access to them.
You shouldn't have any issue riding DME the day after you arrive at MCO...as long as your reservation starts that day.