I spoke with a family who used DME this week, the estimated time for your bags to arrive in your room is 4-6 hours after your plane lands. The family's mother arrived on a different flight from the main group and when she asked if she could just pick up her bags and put them under the bus, they assured her that it was all taken care of.
She arrived at 7pm, they called at midnight to see if she wanted her bags brought up. She chose not to have them brought up and was told that she could get them delivered the next morning after 8 am.
The main group didn't ask and they picked up their own bags and stowed them under the bus, along with several other families. They obviously did not have to wait for thier luggage.
Just an experience from the early days of the program. I think as they get more familar with the system then it will take less time.
Penny