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As the manager acting with owner permission, you're all good to go. There are two primary sections which demonstrate this (which I've cut to save space) -

Sec. 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 handgun, illegal knife, or club if the person is not:
(1) on the person's own premises or premises under the person's control; ...

Since you're in control of the premises during your shift as manager, you're good there.

Sec. 46.15. NONAPPLICABILITY... (b) Section 46.02 does not apply to a person who:
(7) holds an alcoholic beverage permit or license or is an employee of a holder of an alcoholic beverage permit or license if the person is supervising the operation of the permitted or licensed premises;...

§46.14(b7) is redundant if you ask me, but it does show that it's perfectly clear that it's OK for a TABC license holder or his manager to carry at their premises.

Contrary to popular belief, there's no criminal penalty proscribed in the Alcoholic Beverage Code itself regarding firearms, but there's a provision saying that a licensee/permittee who knowingly allows someone to carry a firearm on those premises can have their license or permit revoked. It doesn't apply to CHL holders, cops, or folks like you, either:

Sec. 61.71. GROUNDS FOR CANCELLATION OR SUSPENSION: (f) Except as provided by Subsection (g) or (j), the commission or administrator shall cancel an original or renewal dealer's on-premises or off-premises license if it is found, after notice and hearing, that the licensee knowingly allowed a person to possess a firearm in a building on the licensed premises. This subsection does not apply to a person:
(3) who is a licensee or an employee of a licensee if the person is supervising the operation of the premises;...

Hope this helps!