I've had them move my luggage twice now...neither time was it a terrific experience. First time I was at BCV. I handed them the 4 bags at 7:45 in the morning. The kid told me the bags would get to POR around 2ish. I had heard differently here on the boards, but didn't go into timing with him (I had heard it takes longer). Well, we headed off to MK, got hot, tired and cranky by noon, so headed to POR to check in. Our room wasn't ready, but no big deal. We got some lunch and just relaxed. At about 3:00, I checked with the luggage people, no luggage had arrived yet. POR luggage people called BC, were told that the bags hadn't been sent over yet. Finally, at 4:30 our room was ready. Still no bags...they called BC again and were told, and I quote..."We've been a little busy over here today and haven't had time to move any luggage yet!" POR people were not amused. Said they would call me when they got it. They evidently had to call them a third time before someone finally got in a car and brought just my 4 bags over to POR!!! This was at about 6:00-6:30ish. I just wanted to swim, but since I had no suit, dd had no suit, we just suffered in silence.
The second time I moved from BWV to POP. Once again, I handed off the bags at about 8:00 in the morning and knew they would take a long time. By the time I left POP for the evening, around 4ish, they hadn't arrived yet. But when I returned to my room at 9 or so, they were there.
So, Disney will transport your bags for you, but if you are going to need anything, at all, for the day, be sure to take it with you. The luggage transfer can take 8+ hrs.