Should I ask for her phone number or not?

[David]

I have been working with this girl for over 2 years and I am leaving my job in the New Year. I would like to stay in contact with her because she is a uniquely amazing person and has been a highlight of my time at my current job. I would have asked her for her number ages ago but she has this belief that men and women can't be friends, so I never asked leaving the ball in her court and she has never offered to exchange numbers with me although she has to my knowledge with only my fellow female colleagues.

Since she found out I am leaving she has become distant, we don't talk as much and some days I barely get a hello in the morning, and she prefers to talk to the new guy that has just started. I think that this is just her way of dealing with the fact I am going, but it has been a few weeks now and she hasn't offered me any option to stay in contact and she isn't on any external social media sites, so when I go that will most likely be the last I will see her which would be a great shame to loose someone who has brought joy to my time at my job.

I think I have just answered my own question while writing this, which would be to give her my number and let her decide what she wants to do. What is everyone else's opinion?