Our first trip using DME was in Oct 2009. We were scheduled to get into Orlando at 11:30, so we were prepared to pick up our bags and go to the pick up zone. What we *didn't* bargain on was a 3 hour delay out of our home city due to a groundstop in Atlanta (which at least resulted in all of the last flights out of Atlanta for the night also being delayed). We finally landed at 1:15 am with two incredibly whupped boys in tow. I was worried that DME might be shut down - but when we finally straggled down there, we practically got hugs from the staff. "We've been expecting you! We knew you were having flight issues!"
Our DME driver was just incredible. We were the only ones on our bus (we were going to Wilderness Lodge), and he asked if we wanted the sound for the videos or if we just wanted to sleep. Our poor kiddos did pass out on the way there, and he told us that we could have as long as we needed to roust them and get them off the bus. We checked in at about 2:15, if I remember correctly - I have pictures showing the boys toppling into their beds at 2:30 AM.
It's hard to say how many other people you might have on the bus with you - but Disney really does seem to try to keep the buses moving so that you're not waiting for an overly long amount of time.