Update: It went perfectly fine.
She let me know that she knew I'd need to be seen as soon as she was available (I thought it had been three weeks, but it was actually four since we saw her last, and we had been seeing each other weekly or twice weekly) so she felt it was appropriate to offer a ride.
I got scared that she forgot about picking me up and got a bit sad, but she was just in a session longer than expected. She texted me to let me know she was on her way.
The ride to therapy I was genuinely interested in her car, so I talked about that and did not focus on being nervous. I also talked to my service dog (she was okay with a dog in her car :) ).
She also offered to give me a lift home. I accepted that also and since I had already told her everything I needed to, it was actually much more comfortable on the way home.
I briefly felt awkward during the session because I was complaining about my house (my mom and a hoarding disaster triggering PTSD) but it worked out fine. I realized it wouldn't be awkward later -- I was just worried that she'd feel bad for being forced to drop me off at the house I was complaining about. That was just in my head, I realized.
I didn't talk about therapy stuff in the car (except once to joke about my dad teaching me to not get hit by a car -- which we both know is very ironic because he didn't care if my little brother got hit and he also used cars himself as weapons against us) because I felt she wouldn't get proper payment otherwise. Plus I wanted the familiar four walls.
But yeah, it went just fine. I really appreciated the care.
I hope that helps anyone else who was wondering about this :)