If you use paratransit services and will be travelling to another city in Texas, it mayt be possible to schedule rides in the other city. To find out, call the paratransit service in the destination city, and ask if they allow eligible clients from other cities to ride their system. If the answer is yes, they will likely request an ADA verification form from the transit service in your home city. You will need to call the transit office and make that request.
Please note that the process can take a few days, so plan ahead! Allow at least a week, if possible, to complete these arrangements before you travel. The tickets or passes that you use when you ride in your home city should be accepted in your host city, but be sure to ask about that as well, as services differ from city to city. Also keep in mind that certain areas near or within a city may not be accessible by paratransit service.