You said you got caught or admitted to cheating before so you're pretty much f***d there. That card can always be played. If you ain't been caught red-handed, you may as well just deny to the end and spin it on trust (that's how a broad would play you anyway "oh you don't trust me, well why should i trust you if this is how you think?"), it's better to keep the dream alive. She'll want to believe when things are good so why solidify confirmation of the bad.
If you have to live your life catering to the next person's fears, your life will suck and you might as well go ahead and keep *doing wrong*, because in their eyes you're potentially guilty anyway. You will look guilty because you will be preparing to defend yourself against being accused of what you *didn't* even do.
It's easy to sit here and say, erase and start over, but if you keep bending to her insecurities spawned from your past, eventually you'll be resenting the present.