I'm probably overthinking this...
I go to a gym which is two buses from my house (I don't drive and go to that gym as I used to stay close to it and like it, and didn't want to move). I go for it opening at 6am and leave the house at 445am to get there for it opening.
Transpires that a female who I know from the gym has moved 2 doors round the corner. She has offered me a lift to the gym in the morning, which is very kind of her, but I don't want her to feel beholden - even though we've both being going for 6am starts for years. I also enjoy the morning commute as a time to switch off as I WFH and it's my time out of the house.
If you had offered me the lift, would you be annoyed or think me weird? I don't want to come across as a weirdo!