No, there's nothing wrong at all with starting up a conversation with a stranger. In the OP's case, the personal nature of the questions made her feel uncomfortable and threatened.
I think we all have that internal sensor that tells us when the stranger talking to us is just trying to be friendly, and when they're a potential threat. You're talking about the first case, the OP is talking about the second.
We've all had that moment when the alarm bells start going off that something's not right about the person talking to us, and it's important to listen to those alarms.
OP, there's nothing at all rude about not wanting to share personal information with someone you don't know. If someone's being too pushy, it's OK to get up and move to another seat, maybe closer to the driver. I've done that myself when someone is making me uncomfortable on public transportation. That way, it looks like you're just moving forward because your stop is coming up and you want to be closer to the door.
Very true. I can't imagine asking stuff that personal and I'm a talker.