Not to be disrespectful, but if your significant other can't go to the grocery store without the thought of them cheating is on your mind, you're probably in the wrong relationship to start with.
With that said, in today's world, people are way more open about sex. It's a very, very rare thing that someone will date someone that is a Virginia over the age of 18-21.
This will throw you for a loop... one of my best friends is my high school sweetheart that I dated for 5 years. We live in different states, but when she comes to town to visit family, we'll grab lunch and catch up, usually just the two of us, and my wife is 100% okay with it because she trusts me and knows I'd never do anything in that way with another woman (I'd be sleeping with the fish if I did and she found out, that woman is not to be messed with).