<human>: Can you give me the gist of the text in a nutshell?

Hello Reddit,
I'm an average guy (20M)  who has just gotten out of a long term relationship with My ex, We shall Call her C we  had been together since high school. She was close friends with this girl who we shall call P, P is 18F. 
When C left me, I began talking to P, P is an ex girl friend of a close friend of mine, their relationship ended messily. Because of this I've known P a long time, we are very similar people wi similar ambitions. Therefore I've known her about 8 years. However, I have never seen her as a possible partner until she began helping me out with my own emotional baggage, she is a kind sweet person who is very talented. Because she was C's friend and a mates Ex I never looked at her like this until now.

I have brought up going out and doing things together, such as the cinema a few times. However she has always had to pull a rain check because of work or a prior engagement. This of course is fine. What I want to know is, how do I continually ask her without seeming too, forceful and overly persistent.
I really like her and would really enjoy a relationship with her. I know she kind of likes me too, as she gives me all the correct signals but is it purely because our relationship would strain friendships? I know my friend (her ex) won't mind, as he's engaged to another girl and is happy. And C won't care because she is off doing her new guy friend. 

Help Reddit!
<bot>: how can I ask out a girl who's friends with my Ex? She won't be a rebound, she's amazing.