The Matamoros Medical District operates a FREE shuttle service for medical and dental patients. The shuttle picks patients up on the Mexican side of the bridge, drives them to their doctor or dentist and  back to the bridge when they're ready to cross into  the USA. It's a great, FREE service that gets positive reviews. 
Patients most commonly stay just across the bridge in Brownsville, Texas. Brownsville is a modern city with lots to do and see