@Superfly400,
Single people can date. Dating doesn't necessarily mean someone is part of a serious couple. Dating is just that - dating.
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Offer a bit of sympathy/empathy re the break-up. Suggest she let you know if she'd like to get together for a coffee - suggest a couple of specific times. Do it as two separate contacts.
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Sorry to hear things ended with the guy you were dating. It can be disappointing when things don't work out as we hope.
I'm available if you'd like to go out for a coffee sometime.
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4 - 7 days later if she doesn't suggest a get-together time ....
Hey, hope you're doing well.
I'm around if you'd like to go out for a coffee sometime.
I'm available Sunday afternoon and next Thursday evening if either of those are good and you want to catch up.