I think my lover is sleeping with other people and not telling me

I am a 27yo poly woman with both a boyfriend and a BDSM lover. I think my BDSM lover is hooking up with men on the DL and don’t know what to do. We were hanging out and I saw an email over his shoulder that was a response to an MFM craigslist ad and he quickly closed out his email when he noticed I saw it. I do not care if he is hooking up with other men ( I am bisexual myself) but I don’t want to confront him about this and have him blow up in my face. How do I talk to him about this so that I 1.Feel safe in our relationship and 2.Trust in him that he is being open and honest with me as we agreed at the start of our relationship?

You say, clearly and openly, something like:

“Hey, I need to check in with you about something that’s been bothering me. I didn’t mean to snoop, but a few days ago I noticed you replying to an MFM ad and then you seemed to get nervous and hide it from me. Here’s the thing - I don’t care if you’re seeing other people or seeing men or anything like that. But I do care about secrecy. In order to feel safe in this relationship, things need to be out in the open. Partly that’s about trust, and partly that’s about health, safety, and informed consent.

I’m sorry if I did or said anything in the past that made you feel like you had to hide part of your sex life or your relationships from me. I just want to put it all out there that, as far as I’m concerned, openness is a non-negotiable part of this relationship - and I’m sorry if that wasn’t clear before. Can we talk about what else you’ve been up to, and come up with a way to keep it from being a secret or something that’s hidden?”

If he gets defensive or accusatory; if he refuses to talk about this; if he won’t agree to a relationship with the terms of openness and honesty, then end the relationship - it’s not what you need, and his insistence on secrets like that is a dealbreaker.