Is there a specific rule in texas that says you are allowed to give closing arguments in a bench trial?

I do not believe there is a specific rule permitting it - and even if there was, the judge could limit your time to 30 seconds if he really didn't want to hear argument. HOWEVER - rather than announcing simply that you rest, you might instead say "based on ...(make your brief argument), the State rests. Defense could do the same thing, then you close. Of course you are in the best position to determine how your judge might react to that. You could discuss with defense counsel so you and they are on the same page.