Edit2: received advice which I appreciate but am open to more

Background and Event

Not sure how much detail to divulge, but here goes. I'm 27, fully inexperienced sexually (the dreaded v-word), but I am ready to fucking rock. I have been self-improving, reading lots of TRP for about 4 months, lifting, and so forth. I saw a woman tonight who I saw only once before several months ago. I wanted to do something then, but got cold feet. I am not like that anymore. So, when I saw her less than an hour ago, I went straight to it. After talking for a bit and getting some positive vibes, I asked her to hang out. She was a little nervous and giggled some before saying yes, but that she is engaged. She asked if I was cool with that and then she said that we could be friends or something. I was pretty bummed at the moment, but she said she has friends and younger sisters she can bring out. Also, you never know what could happen with her. For the record, she is 28.

Questions

So, right now, I have her number and she doesn't have mine. What should I do in this situation?

(Examples: Message/call her later this week so she has my # and leave it there?, message/call this week and cultivate some back and forth to feel out if she is DTF?, if so, when?)

And, whatever option you think is best, how should I go about things? How to ask/find out if DTF?, Ask her outright to hang one-on-one? Minimal speech or cultivate some sort of friendship so she gives good word to her sisters and friends?, etc. These are just possible answer examples I'm thinking of.

Thanks and Addition

Thanks, everyone, in advance for your help with this.

Edit (addition): Forgot what could be an important point. Before we separated, I made a joke saying, "Yeah, bring your friends and sisters so your fiance doesn't want to kill me." And she replied, "No, it's okay. He wouldn't do that. He's a nice guy." Possible hint that he is beta and she's looking for some on the side?