Is there a point to your (incorrect) post?
You've misunderstood OP and my post, and where locations are.
The woman does not live in the opposite direction from venue to OP. Woman lives 5 mins past OP from the venue - ie OP has to go from venue, past where she lives (5 mins) to woman's house and then back to her house (in direction of venue)
Woman lives 5 mins from OP but they both live in the same direction away from venue (that's how I've understood it)
Bus to/from venue irrelevant
There may be a bus from near OP house to woman's house, if not, she could get a cab from OP's address which would be cheaper than from venue.
The 'logically' comment is not logical at all - we know there is a bus that goes from woman's house to venue as OP says she assumes that's how woman gets to venue.
What we can deduce, logically, is that journey = venue - past OP's home (or thereabouts) - woman's house. Therefore, any bus stop from venue to OP's house (or thereabouts) is nearer to woman's house and, with my logic, that could be helpful
Your helpfully bolded reply is based on this incorrect premise:
"If the OP went straight home, she (the OP) would actually be taking the woman further away from where she (the woman) lives."
I've read it that they both live in the same direction away from the venue but the woman lives 5 mins further away so OP has to drive 5 mins further and then 5 mins back on herself to get home. I may be wrong but if it is the way you've assumed, why would OP have offered a lift originally if she lives in opposite direction.