Our kids have been riding the bus since they were little, though less often since we started sharing a car almost four years ago. For a while the oldest, age 10, has been asking when they could start taking the bus on their own. A few days ago they did, and it went well!
We worked up to it gradually, so they knew how to do it and we knew they knew how to do it. They had a background experience of having taken this specific bus many times, though mostly not paying attention. Once they said this was something they wanted to work on we switched to having them lead: they sat by themself in front, and we sat in back. They handled keeping track of where we were and pressing the "stop requested" button.
We did this twice, which they handled well. They got us on the right bus, paid attention along the route, and got us off at the right place. The only problem was that both times someone else happened to press the button for the stop before they did, so I wasn't totally sure they'd remember. But they thought they would, and I was pretty confident that they would as well.
They day before they rode by themself for the first time we talked through the process: walking to the bus stop (0.5mi), how they'd know which bus to get on (94), how they'd know their stop was coming (first crossing the tracks, then going up the hill), what they would do if they missed their stop (walk back along the route), and what they'd do if someone asked about them being alone (I'm going to my grandfather's). Then we did it again that morning before they set out. And it all went great!
They also had their watch in case there was a problem, but they didn't end up needing to call us.
It's great that we and they now have this option for getting to their grandfather's house!
I was wondering whether this was a typical age for people to start being able to take the bus solo, and remembered that I did a survey on this kind of thing:
It looks like 75% of people thought a mature 10yo could learn to handle public transit solo, and 40% thought a typical 10yo could.