It is not in any way illegal to have a baseball bat in public.
§ 46.01. DEFINITIONS. In this chapter:
(1) "Club" means an instrument that is specially
designed, made, or adapted for the purpose of inflicting serious
bodily injury or death by striking a person with the instrument, and
includes but is not limited to the following:
(A) blackjack;
(B) nightstick;
(C) mace;
(D) tomahawk.
§ 46.02. UNLAWFUL CARRYING WEAPONS. (a) A person
commits an offense if the person intentionally, knowingly, or
recklessly carries on or about his or her person a (...) club (...)
Now, if you specifically adapt a baseball bat for the purpose of striking a person (and inflicting serious bodily injury or death), such as sawing it off, setting spikes in it, attaching a wrist lanyard, etc., then it could be ruled a "club" and be illegal to carry.