Your situation is almost exactly what my W did. Hers was with an old BF she knew before me. It lasted a few weeks of heavy texting and phone calls, during vacation too. All started "innocent" same as you. He started with the sexual innuendos, seductive talk, probing for where it could go. She liked the attention and the compliments. Blah, blah, blah. When I found out she lied about everything. And kept lying, and may still be. It took 6 months to get an admission she even met the guy even though I knew she did. Then 2 more months when the OM sent me a pic of another meeting they had. Again denying she met him. And 2 years later we are still together I don't trust her fully and when I think about it I get angry.
So whatever you do....DO NOT LIE! Tell the whole story, don't leave anything out, answer all his questions fully, don't downplay what you did. If you want him to trust you, you have to be trustworthy, little things and big things.
Realize that you are responsible to rebuild the trust and the timeframe is how long it takes him to trust you. The length of time will be partially dependent on your actions and partially about him. You can only do your part. Actions are better than words.
That is one part. You also have to explore yourself and determine why you did this and fix your issues. If you have some low self esteem issue and need the attention from OM's then you need to fix that or you may do it again.
I am working on me and really digging deep. I know my selfishness and self-centeredness is a big part of what brought me to this point. It was all about me. He was doing his part to work on giving me what I needed and my selfishness only saw what I wasn't getting.
I am doing everything in my power to be 100% transparent. My relationship with this guy didn't get very far, thank God, but I he really believes there is more to it and that more information will come out later. I guess only time will tell, but I really have nothing to hide. Thats one of the hardest parts in this, is getting him to believe there was no physical contact and no intention for any physical contact either. I get my actions are the only thing that can prove that, just doing my best to find the right actions to prove it.
