Personally? I wouldn't pursue it with her. It's done, the trust has been fractured and there may be no return to the closeness you thought you once shared. You can choose to have her as a friendly acquaintance or not. It's up to you.
One of the more difficult things in the dissolution of a long term relationship are the side effects. :sigh; This feels like a side effect to me, and as such would be best moved away from.
At the risk of sounding really harsh, you need to focus on yourself now. Totally and completely yourself (with regard to all adult relationships) and if you are not completely comfortable in all aspects of any adult relationship, then move the necessary distance from it. Some relationships you will be able to maintain at arm's length, others you'll have to move away from completely. Just be certain to focus on what YOU need now. It's about time, eh?