<human>: I met a buddy for happy hour a couple weeks ago and it turns out he kind of knew another group that was at the bar. It was a guy, his gf, and other girl (og) I walked in and sat next to og. 

It turns out her and I have a bunch of mutual acquaintances and she works in a field where I'm potentially a client for her. She's well versed in my industry so we talked about that too. It was going great.

The guy got weird and insisted they all leave suddenly. I asked and she gave me her personal number. I never messaged her.

Fast forward two weeks to today and she emails me from her work email.  Please keep me in mind if you need my services, etc. she then wrote "it's crazy how many people we know. I really enjoyed talking with you and I hope I run in to you again soon."

I responded to her work email and apologized for not messaging her, but explained that I got caught up in the holidays. Told her I'd keep her in mind if a transaction came up. I made a dumb joke about it being a small world. All good. Here's the part I feel cringey about " I hope it's not inappropriate, but I really did enjoy talking with you, can we have dinner this week?"

It seem s innocent enough, but I feel like sending that to her work email was a bad idea and now I'm feeling weird about it. I sent it after 5, so I'm sure she won't see it until tomorrow. I've had a rough patch dating lately and am feeling a bit insecure too. I'm sure that's not helping.

Was it inappropriate to send that to her work email? Did I assume her email was flirty and it wasn't? Am I just over analyzing this?

Could you distill the essence of the text into 1-3 sentences?
<bot>: got a girls number, didn't message her. She emails me two weeks later semi-about work and I replied asking her out over work email. Now I'm wondering if that was creepy?