A legal connection at DFW is 40 minutes, so theoretically your bags should make it.

If the bags are left behind, you will have to fill out the necessary paperwork at the SAT baggage office and you should have your bags within 24 hours.

Twice now AA has delivered my bags from PHL and LGA to central New Jersey and in both instances, the bags arrived the next morning. The delivery service even called in advance before dropping off the bags. It does not seem to matter whether the delivery address is a residence or a business.