Helping out a friend... I need advice on what I should do to gracefully get out of this.

Just a different take on grocery shopping. I live on a farm a long way from shops, and I go shopping once a fortnight. Early on, I made this easy by switching to UHT milk (we buy a dozen at a time), milk powder for cooking, 20 pound sacks of breadmix plus a bread machine, and a large freezer (vertical is easier to deal with) for meat and frozen peas, corn etc. Many locals freeze shop bread as well.

‘Gracefully’, you could suggest that she sets this up, even offer to help her do it. You are becoming too busy to be able to make this regular commitment. If she won’t accept this (which is probable), you know that this is about ‘want’ not about ‘need’. Then you find that you are too busy, you are sorry that she didn't want to cope the way that others do, and she should find a live-in facility where her shopping ‘wants’ can be dealt with in just the way she would prefer.

Your friend is at an adjustment phase of life. Adjusting to a little loss of independance.

When my relative stopped driving, the choices were 1. Senior bus 2. Taxi/Uber 3. Family/friends.

There is no option called 'adult children or friends MUST now be the chauffeur'.

This also applies to setting up grocery deliveries, or any other assistance that is required.

Regarding "She refuses to do it".

That can be denial. Fear of change. Pride. Maybe inability to master the new skills required (eg for online groceries).

If you want to stay a friend, stay a friend. Gently return your relationship to that of *friendship* not chauffeur. Put in reasonable limits. Eg Yes to driving if you go out for lunch together. No for her daily driving needs. That is up to her to source.

Sometimes people get what appears to be selfish about their needs. They don't/can't see they are becoming a burden on others. Afraid of change.

If that is where your friend is (you are not her shrink either by the way) suggest she call an Elder Service for ideas & services. Hopefully with the right support, she will start adjusting to this next stage of her life.

Been there, you volunteer and then its felt you have all the time in the world to help them especially when ur retired. I stopped volunteering. If asked, I will probably do, but I can say no the next time. My new saying is "I am here to to help people find a way, but not be the way".

Call your office of Aging and see if they provide bussing. If your friend can't walk the store most supply scooters. She maybe able to call in her order and have it delivered. You may need to be honest and tell her your not willing to do her shopping indefinitely. Me personally, I hate to grocery shop. So I wouldn't volunteer.

There's a reason she isn't driving. She's AFRAID to drive, and likely for very good reason. My brother was much like this in that he was unwilling to set up anything to do online shopping, which is all that could be done where he lived, had no computer, etc. Never got into the 21st century. He lived at the end in a lovely small trailer part that was historic, quite beautiful, in So. Cal and he had all these neighbors who, when he was first diagnosed and was recovering from an accident in rehab,said to him "Just call us, when we go shopping come with us, or let us know what you want". He and I BOTH knew that this was not wise. His decision was to move to assisted living and it was a GOOD decision on many fronts. I lived at the other end of the state. There was no good support system; his balance had been off for some time; there would be no more driving.
I know you meant well. Now you are roped in. This will get worse and worse, not better and better and your friend will become more dependent. It is soon time to have an honest conversation with this friend. She will have not to depend upon friends for care. If she needs care she may need to change her living situation. It is terribly sad and terribly hard and believe me, I KNOW that, but it will come to that, sooner rather than later.