Yep... that's what I say. Just stop her and ask her one day. Maybe have you name/phone# already written out ahead of time and hand it out the window to her.
I know the bus runs on a tight schedule for school. So, you don't have a lot of time to be playing around. Plus, if she is a "good cyclist" aka follows traffic rules... she should be stopped just like traffic when the bus stops if for kid drop off and pick up (the cross arm is out--I personally stop on my bike).
If you are kinda just yelling out the window on slow drive motion, she might not hear you. Could take a second. I know when I go to talk to my kids' bus driver it's hard to hear cuz the bus is so big and loud.
You don't want her to get sucked in riding next to you passing either. She might be too freaked to listen. Just some thoughts if she doesn't seem responsive--it might not be you or the idea--just trying to focus on traffic instead. Or if she does--some peeps just prefer to ride alone (head clearing). But, you never know until you ask, of course.
If ME, I'd just say, "HEY! I don't mean to seem like a stalker, but I'm a fellow cyclist looking for a riding partner--just wondering if you might be interested?". Straight up is good in my book.
Good Luck!
EDIT: Side bar note... If you do become her riding partner, you might teach her something I learned here on TE. That mixing up your routes is a good safety practice. Specifically in relation to being stalked. One of our local tri gals was ran off the road by a man in his car, raped, and left for dead (her fitness level and ability to fight him off/endure afterwards was an attributing factor to her being alive, btw). She rode the same training route. Just like you see the same lady, same time, same place--on your same bus route. A good safety tip to pass on. Not to be paralyzed in fear--but just trying to be more aware of your practices and surroundings.




Good Luck!
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