You will need just a valid Texas hunting license. It can be just a small game 5 day permit or the full non-residents with all the big game tags. Other than that you don't need anything special for bobcats. No season and no bag limit. To transport out of state you will need a CITES permit to cross out of the state with it. You can get these for free through the Texas Parks and Wildlife Department.
Enjoy Texas, and have a great Thanksgiving.
Good Hunting, and God Bless,
Byron