Is there a chance you were not the real target?
If she was in the room, you needed to go engage her in person and get her number yourself.
Using a friend as an intermediary is grade school pussy bullshit.
You need to go get to know her in person, before you propose going to do an activity.
I assume you are talking a gun range? The way you do that is you mention that you are pretty busy in the upcoming week. Tell her that you need to make some time to sight in a pistol or rifle or shoot some trap. IF she responds that she LOOOOVES to shoot or always wanted to learn, then move forward with "well, I'd be happy to take you...How about next Saturday?"
Your interaction will make her give you hints about what will get her out alone with you. Listen for the clues. This time of year looking at Christmas lights is cheap and easy. Going to an outdoor christmas chorale concert.
She might be recruiting a New years Eve date.... Feel that out,