You can get your luggage the night you arrive. But, it may be pretty late. Only you can decide if you want your luggage delivered to your room past midnight. I would actually not tag my bags. I would pick them up myself at baggage claim, rather then have DME deliver them. Then you can take them with you..the bags will go underneath the bus. If you choose to do that, do NOT put the yellow tags on the bags you will be checking!
There is just no way of telling exactly how long it will take your bags to get to you....could be within two hours, could be more than that. But I would think that they would be there before midnight in all likelyhood.