She initiates first and seems interested. Do I send a friend request because I wasn't able to finish the convo at the store?

She initiates first
So I'm in a store, and this woman who I've seen once in gas station, just happens to be the cashier in the line I'm in. I had just got through working out, and have my tank top on, with my arms and shoulders shown lol.. anyway, she rings me up.. as I put my stuff on the register and she starts scanning, she asks me how my day was, initiating conversation. With a slight smile. I kept it small talk because there were folks behind me and didn't want to bring too much attention to her and get her in trouble. Keep in mind this is a small town, maybe a small city in a year or two. Not small as in hicky town small but smaller than a small city. I remembered her name, found her on FB as she is the first person to pop up on search. I wanted to really give her convo in the store but couldn't. I felt like she was interested especially initiating. Would it be wrong or weird to send her a friend request? Ladies especially need your opinion on this.

She initiates first and seems interested. Do I send a friend request because I wasn't able to finish the convo at the store?
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