Strawda, first you have to understand that this is a marathon, not a sprint. A lot of your answers if you work the process of healing come about in their own time. Can't make the answers appear. Although we have all tried that!!
If you ever saw the movie "What about Bob" you have to take baby steps first.. There is no "Proving love". Your BS is right in saying you need to work on you before you can really help her. You can be supportive to her, but you need to get into IC, reading books, posting on SI to find out what allowed you to think it was ok to cheat. These ACTIONS will show her more than any words can.
Are you doing any or all of the above?