How long has it been since she split with her ex?
Like others have said she may still have feelings for him, and if it was a long, close relationship she may always have feelings for him, although these will hopefully, gradually fade to caring more than loving feelings. Give her a bit of space and then sit down and talk to her about it. Tell her exactly how you feel, and find out exactly how she feels, and then take it from there.
You seem to really like her, and seem a caring and patient boyfriend and so I hope she realises this and that things work out for you.
Good luck!