Public transport is really expensive or terrible these days, which doesn't help. When I started hillwalking, I didn't have a car, and I often used to take the train to the hills - the West Highland Railway. Now that railway is unaffordable!
If you join a hillwalking group on Meetup you can usually find someone to give you a lift in exchange for a contribution to fuel, but you usually have to get to a city first.
I should say hillwalking or climbing group - the climbing Meetup group that I'm a member of does both.