The drive in a personal vehicle is not the same as it is in a commercial shuttle. The drive from William P. Hobby Airport in a commercial shuttle and not a Corvette is 45 minutes to an hour and from George Bush Airport the drive in a commercial shuttle and not a Corvette is about 1:20 if there is no traffic.
Also, you are probably judging the time from the highway without considering the shuttles actually are loading up at the airport before they make the ten minute drive to the highway. There is also a ton of traffic on Harborside and Broadway you are probably not considering. Please also understand that these times go completely out the window when the motorcycle or jeep rallies come to town. Forget these times also during spring break weekend as the population on the island explodes and traffic is a nightmare.
I'd say at midnight, and with a police escort, you can make it from the Hobby Airport exit to the Galveston Cruise Terminal in about thirty minutes, but not from the commercial passenger pick-up area at the airport.