We just got back from staying at the Hyatt regency. It has a shuttle that costs but the staff is very friendly. My only caution would be that it starts running 45 minutes before the regular park opening time. That means if you have a ticket with Magic Morning, it does not get there until at least half an hour after the earlier hour. For example, when we were there the park opened at 10 am. We couldn't get the shuttle until 9:15 am and it was about a 10-15 minute ride. The earliest we arrived was 9:30 am and then we had to wait in security lines.
It wasn't a big deal for us since we were traveling with small kids and moved slowly anyway

but it may be a problem for those interested in using early admission.