There's nothing said of wanting to live an isolated life.
OP's friend clearly goes to work and socialises. So, she clearly doesn't want to be isolated. However, is she truly not allowed to have any boundaries at all just because someone offered her a lift? For all we know-the friend does other favours for OP in return or has helped massively at work with OP.
Regardless, OP is willingly allowing this friend into her car and giving her lifts. That is her choice. Equally, her friend is free to decide who can and can't enter her home and it is her choice. She doesn't need to stipulate a reason and whilst it may seem, on the surface, mean, it is her right to do so.
From what it sounds like, OP was well-aware that this boundary exists and shouldn't have had any hopes of it being dropped. If it's an issue for OP and she feels it's "rude/mean/whatever word you want to use" she can make the choice to not offer lifts in future. That is her right.
However, someone doesn't get to break someone else's defined boundary just because they did something nice for them. That's not how life works. There could be a multitude of reasons why this boundary exists, and OP can either ask directly about it and be prepared to be told to mind her business, be told the answer, etc, or she can mind her own business and decide how to proceed with the friendship going forward if this is such a big deal for her.
Would I leave someone in pain/discomfort needing the loo? No, of course not but I'm not OP's friend and don't have her specific boundaries.