@Piers Nivens I think your planned convo opener is fine. Be aware and prepared for her to mention that she is seeing someone else.
Your only response to that is "I understand."
Then you simply ask her out to dinner anyway. If she balks at dinner then your only response is to make it about you. As in "listen, I know this is on me. I realize I was out of line. You are a great person and a great woman and I am serious about us moving forward and accomplishing great things together. How 'bout I pick you up on x day at y time."
You might not have to put it on the line like that over the phone (and in that case stay with your planned convo.)
And if she has started seeing another man the details are NONE of your business so do not ask or inquire about that. You sent her away, she's a high quality woman, so you are responsible. Get over it in advance.
She invested years of her life in you. Hopefully the positives (because surely there are) are enough for her to come back.
FYI I'm a chick old enough to be your mum. I've been in her shoes. I'm telling you what I would need to hear to give you a shot.
And if she gives you the opportunity you need to be thankful (not in a 'beta' way) and move forward together with respect and purpose and self control.
Become the quality man you are capable of becoming. You can. Perhaps with her by your side.