If the OP never attended this group the woman would have to pay for public transport back so she should give that money she has saved to the OP
Not quite. There are rules around accepting money for giving lifts - for both insurance and tax reasons, it can’t be any more than the actual cost of taking the car on the journey. HMRC accept 45p per mile as a reasonable estimate for that, with no evidence of actual costs required. If the bus fare was that, or less than that, then the woman could indeed give it to the OP. That might make her think twice about needing the lift so much.
I regularly give lifts to people who are not friends, colleagues or even known to me. I do it through a charity, which organises everything. And I receive 45p per mile for every mile I drive. The intention is that, although I give my time freely, I should not be out of pocket for the use of my car. I also give lifts to other members of my walking group. The organiser of that has a rule of thumb of 25p per mile, to be shared between all passengers, with the driver not counted.
Both of those recognise that there is a significant cost to running a car - it is not just the petrol, it’s the servicing, tyres and so on (which are mileage related), insurance, tax, and - the biggest cost of all - buying the thing in the first place.
It is good for lots of reasons for car journeys to be shared. But it is not reasonable IMO to expect the driver to bear the full cost - even if it does not involve them going out of their way.
Note that the OP does not describe the passenger as a friend. She’s just somebody she met through the hobby group. She should feel under no obligation to offer a lift at all if she doesn’t want to. If she chooses to, it is perfectly reasonable to ask for a contribution.