There are two airports in Houston. Bush Intercontinental (IAH) and Houston Hobby (HOU). The Port of Galveston is 70 miles from IAH and 54 miles from HOU. The cruiselines will provide transfers from IAH but only Princess who is only there part of the year will porvide transfers from HOU. Since Southwest Airlines flies into HOU I'm assuming that was the great rate you were referring to. Carnival and RCI won't pick you up there.
I refer clients to a service called Galveston Limousine Servive. Their phone is 800-640-4826 or go to galvestonlimousineservice.com They offer motorcoah transfers from both airports and are normally lower cost than the cruiselines.
Happy sailing, Neil