Here's what happened. The bulldog was terrified of the ride but walked into the vet's office with no problem. First, she pooped on the floor which was good because she hadn't gone since she arrived on Saturday. The vet checked her over and said he didn't see any problems and that she was healthy. He estimated she was 4-years old, but after I got home, I found out that Bulldog Rescue had tracked down her vet and that she was actually 7-years old.
I went to the front to pay and she piddled on the floor, which was good because she hadn't gone since she arrived on Saturday. I went out the front door with her and thought I'd try to take her for a little walk. We started out and she ran at full speed to the end of the little strip mall and then stopped. Then she turned around and ran at full speed to the other end. Taking advantage, we went around the back and all the way around the place. So, she seems to be in OK shape.
When we got home, she went right up on the couch but now she's actually drinking water and ate a bowl of kibble (both on the couch.) I'm gong to try to take her for a walk today, because she's still terrified of the back yard.