I called Guest Services at HRH. At first, I was told that there was a HRH shuttle (complete with logo on the van). I asked if it was free, and he had to check. Then he came back and said that it was $13 one way.... I asked if the shuttle would be identified as a HRH van, and he said no, Mears handles everything for them. (Not too impressed with Guest Services so far)
Mears has shuttle vans that leave the airport every 15 minutes or so. I went online to check the fare for the time in April when we plan to visit: adult - $23 roundtrip, child - $16 roundtrip. Their phone is 800-759-5219 (busy when I tried to call); their website is mearstransportation.com, and you can make reservations online.