Or is she another lost cause?
It's hard isn't it. What to say, how to say it.
Sounds as if she is a nice girl and good for you to have the courage to ask for a date.
If you get rejected remember, it will happen time and time over, but it will also happen whereby a young lady will say yes, because she would like to get to know you.
If I was you, if you get rejected, don't go for the friends zone, your wording comes across as a possible "stalker" not that you mean that, but it can be a bit scary...and if not not, trying to get into her pants not getting to know her.
Trying to get with you .
But ah, stuff it let's just be friends.
Wait, I don't know you, you don't know me, so friends first then let me try to get with you.
Wait, I'm done, forget that, I just wanna be friends.
Is that Ok?
If rejected, smile at her the next one when you see her, act confident and turn the other way and keep walking.
At some point one lady will find a way to then talk to you, talk...