From what I read you have a couple of problems...First, if you defined your relationship as monogamous, by having experimenting and quenching your desires, you breached the understanding and trust that is defined by that understanding of what the relationship entails.
If you could not achieve some sort of acceptance from your girlfriend before the incidence and make her part of it in some way you are guilty of being not only unfaithful but also selfish.
Now you are looking for forgiveness under the hopes of compassion. Wow, what planet are you on?
What would you do, and how would you feel if the situation was reversed?
Breaching trust is never a good thing and not a sign that you truly love that person. Asking for forgiveness and getting it will never bring back that trust. What you need is understanding….Ask for that, but don’t ask someone to value something that you discount.

__________________
Sex is a tricky thing best left to professionals.