Untangled, your position is both reasonable and understandable.
But on the positive, her wanting to be friends with perhaps a view to reconciling has given you the opportunity to put an iron in two fires. Tell her that you will be friends, but will start dating again. Tell her that if and when she decides to try again, you will consider it if you are available. You must not give her all the power to dictate your future.
If you approach like this, there will only be good outcomes for you:
1. she will freak out about you dating other people and want to get back together.
2. she will agree to it ...giving you the opportunity to wait and see what happens while also getting to see and trial other girls. You may well find someone you like better.
3. she will refuse and not be friends and not get back together - which would only prove that she was trying to have her cake and eat it too. And that she only wanted to keep you around as sad ex lover/friend.
Never regret anything that has happened in your life. It cannot be changed, forgotten or undone. So, take it as a lesson learned and move on.