When I started I used to hit a lot of checkout girls, I got ripped to fuck on here for it. In hindsight probably desrved.
Having said that the experience taught me several important points:
Don't trust IOI's its there job to be nice.
Of course be persisitant, just be aware that she is trapped and has no where to run to, work out if you should back off of go for the finish line.
and finally leave checkout/till girls alone
Flirt with them make them feel good about themselves but hit on the the girl putting bananna's in her basket instead.
Someone has already said - (quiet randomly i asked her) If iam not being too forward can i ask you for coffee?(I'am trying direct approach)
This is wrong too AFC, try something like there is a great coffee place round here, you ever been? What time you finish? Look meet me outside I'll take there.
To end on a positive note maybe what she was trying to tell you is she was bored with marriage, women say the strangest things in the hope we'll get the clues.