Generally the court's bailiff will call your name one last time before noon (at least in Dallas Co) and then will inform the court of the defendants that failed to appear. Bench warrants or bond forfeitures will be issued at that moment. They generally hit the system anywhere between immediately and a few hours. Sometimes even the next day if you're lucky. Call the court NOW or go up there, apologize, be prepared to have your bondsman go back on your bond or hire an attorney NOW and go to court with them to request that your bond be reinstated. You need to handle this right away. There are several attorneys from San Antonio on this forum, including Shannon Locke. Give him a call and see if he can offer you advice or help you. Take care of this now though or you'll be dealing with added charges.
Generally the warrant issues that day. Get a lawyer to help you out before you get arrested. It is better to take care of it than to get arrested.
In Bexar county, it depends on the court. Some courts will issue a warrant immediately and some may wait a period of time, generally 10 days. In any case, you do need a lawyer. I would get a lawyer and have that lawyer go in and plead your case. Maybe there will be no consequences, maybe the bond will be raised and you can then make arrangements.
Regardless, things will be much better if you go in and explain the situation as opposed to getting arrested.