Should I give this girl my email or would it be too much?

I'm probably overthinking things here, but I wanted to get a second opinion.

Long story short, I met this girl at my last job and she left the company for a full-time position. She was really cute, sweet and hilarious. I never spent a lot of time with her but I had a crush on her and wanted to ask her out. I never did but I also have a policy of not dating co-workers. Late last year I ran into her again at a work event (she was there volunteering) and I wanted to send her a message afterwards saying it was good seeing her. The only way I have to get in touch with her is Linkedin and I know that's not a site for dating, but I at least wanted to send her a message. It's been a few months since and I've finally decided to work up the courage.

I finally sent her a message and then later in the day, I ran into her at an event. She answered my questions there and she sat in front of me for the event (a speaker) and my heart was pounding. It's amusing and annoying that I feel so nervous around her, I went to the bathroom and was going to leave before I made a fool of myself. Sure enough, I ran into her as I came out and we talked a bit more. I said we should grab coffee, she said "yeah definitely."

I want to follow up with a new message and give her my email. What should I say? Should I offer her my email or is that too much?