Most of the above are jokes...to be expected. Some well intentioned but hopeless advice in there
You cant talk to her when she’s driving. There are a few reasons for that, but let’s start with that as an assumption
so then, when is she not driving? When she is stopped letting people on and off the bus, yes? That gives you two opportunities to interact, getting on and getting off. So let’s examine those. Which one do you have her attention? If you answered getting on, you’re doing well. This is for an obvious reason - she is responsible for monitoring those getting on, ie making sure they pay. Other than safety she has no responsibility for those getting off.
So now we are narrowed to getting on the bus. You need more of an interaction than the three second window you have to swipe your card. Here’s what you do. Don’t take the bus for a week. Figure something else out. The next Monday, you get on the bus. Dress nicely. Be the last in line. Have a coffee in one or those cool stainless vacuum thermoses like a Zojirushi. Your card is not where it normally is, you’re now checking all of your pockets, ask her if she doesn’t mind holding your coffee for a moment, and finally you find it. Apologize, let her know you spent the last week traveling to Nepal or some damn place and just got back last night, and leave it with “I owe you one”, be sure you got good eye contact on that exchange.
When you get off, give her a “thanks again” but don’t linger on it.
Bext day, again get on last (make that a habit). Have the card out right away, something like “no need to fear, I came well prepared today...” should be delivered with a little theater and a big smile. Now this is a key point. If you get a big smile back here, you are exactly where I intend you to be. Anything else (no smile or halfhearted / forced smile) and something went wrong. But if you have followed my words and delivered them convincingly, and don’t look like a gargoyle, you should get that smile back.
If you got that smile, pen a note while on the bus. Nothing lengthy, something like “hey, I told you I owed you one for helping me out yesterday. I would love to take you out for a drink and some conversation. Talk soon”
and your first name and phone number. Give her the note deliberately when exiting, with another smile.
Last point, at some point (and it could be after three months of dating) it won’t work out, so be sure you don’t depend on this bus route for your commute.