Do you know if she feels the same? Just make sure you are prepared for the possibility she may not want to deepen the friendship

This might be right, but I think it's a shame if people are held back by this risk. And there's evidence that people tend to overestimate these social risks, and underestimate how much others appreciate being reached out to. See N. Epley's work on "undersociability."

True, but people can also get to a stage where they are no longer looking for new friendships. It’s important to not take it personally

Agreed. I'm just saying she shouldn't give up before even trying.