Here is the info listed on the Hyatt Cypress website
Arriving Guests: Upon arrival, please proceed to Ground Transportation, located one level below baggage claim and look for the Mears Transportation desk. Inform the representative that you need the shuttle to the Hyatt Regency Grand Cypress. After hours, you may reach a Mears Representative for assistance via the phone located at the desk.
Departing Guests: Mears provides direct transportation from the front entrance of the hotel to the airport. Advance reservations are required, and can be arranged through the Mears desk each day from 7:30a.m. - 8:30p.m., or via phone 407-239-1234 ext. 4149. After hours, please call 407-423-5566.
Cost:
Age 12 and older $20 one-way, $33 roundtrip
Age 4 11 $16 one-way, $26 roundtrip
Age three and under are free