My one and only experience with staying at an offsite and using the hotel shuttle was horrible. This was several years ago and our first trip to Disney "with kids". My daughter was 4 1/2 and my son was 21 months and we had a stroller with us and of course all the "accessories" that comes with young kids, LOL.
We stayed at the Doubletree Guest Suites Downtown Disney, and the shuttle bus served all the hotels there on Hotel Boulevard. The schedule was a few trips over in the morning and a few trips back in the evening.
Well around 7 or 8 pm it started POURING rain, got chilly and nasty, so we decided to go catch the shuttle back. WRONG! There was one that left just as we got to the transportation lot, packed full like sardines. We crowded with dozens of other people under the shelters and waited for the next one, almost an hour later. Talk about a stampede! We didn't make it on that one either. By this time it was after 9 pm. I was standing there in the rain holding my then sleeping son in one arm and had my daughter's hand in the other, my husband was juggling all the strollers and "accessories". Another hour goes by and a 3rd bus comes, we take off towards it like maniacs (as did lots of other people) and literally had to fight our way onto the bus.
It was almost 11 pm by the time we finally got back to the hotel. It was a horrible experience, and I'm sure not necessarily the norm, but I vowed to NEVER depend on shuttle service again. I don't like being so out of control of a situation, LOL!