I don't think your expectation is big. When I was 13 we visited London for the first time. (A different continent to where I was raised.) We stayed there for 3 weeks, and by week 2 my brother (14) and myself were riding the subway without our parents. (It really isn't that hard to figure out.)
But equally by 13 we'd had a lot of experience with public transport at home - busses home from school, or into the city, and so on.
I don't think age has terribly much to do with it. Exposing kids to the process, making sure they have the tools to deal with the unexpected. A small amount of emergency getting home money - these days a phone obviously - and I'd likely toss in a tracking device of some kind (in addition to the phone.)
I think you are on the right track. Get them familiar with the options, and then slowly get them more involved. They can buy the tickets - identify when to get off. Perhaps "miss" the stop a couple times to show what happens if you do, and so on.
In some countries letting the driver know where you plan to get off is good if you're young. Don't rely on it, but in lots of places drivers are happy to keep an eye out. (And you don't have to be young. I caught a bus in Norway once with no idea of when I was getting off, I just told the driver and he stopped at the right place, and let me know it was my stop - I was probably 35 at the time.)
For children, it's not about age, it's about experience. Once they've got the pattern down, the age really doesn't matter at all.
(Ironically, looking back, I don't think my folks ever rode the bus with us. It was more like - "there's the bus stop, here's money for the fare, get off at the right stop - how hard can it be?" :)
