Yes, Galveston Saltwater Moms will pick you up from there. Just be sure to contact them ahead of time to get in a reservation. The other thing to mention is it is best to pay cash. They aren't set up for credit card payments (or at least they weren't) unless you want to send them payment thru a pay app. You can ask about payment when you make your reservation. Or you can Lyft to the port. There has been an issue sometimes with using Uber.
I agree with you. I've used Galveston Saltwater Moms 20 times so far. And have 20 more reservations. I trust them so much more than Uber, Lyft, or a taxi. And yes, they are insured.