I agree with squirrels when he says "Popularity is relative". It's your own perception of her. Maybe some other guy thinks she's a clown, another guy things she's just out for attention, and yet another doesn't think anything about her. Don't let your own assumptions throw yourself off.
As far as the "If she blows me off, that won't stop me from trying again"...you sound like a stalker. Go in there, talk to her, see what happens. If she's not interested, respect that. Then maybe you can chat with her here and there when you come into the coffee shop and see if something develops after she gets to see you more often.