When trying to trust again would you say it is okay to ask your bf to show you his phone and text messages?

We have had a heated discussion prior. I had done the big no no and looked at his phone. I saw many texts and flirts on his phone with other women. I've since then worked on resisting the urge to look. He's got a password on his phone now and I just have this feeling he's hiding something.
I finally got him to understand his texting and comments towards other women are very hurtful and disrespectful to me. Makes me look dumb and I can't take it. He got upset saying he's not cheating on me. He's had plenty of offers of sex no strings attached offers and he hasn't done anything. Texting isn't cheating. I agree, but it IS disrespectful and rude and I don't deserve that. He refused to see himself in the wrong. I left for a couple hours very ticked off. When I returned he came to me held me and apologized. Promising me he will not do it again. I just feel like he's hiding something. He will not leave his phone alone with me and I feel something is "off".
I've always been right about this feeling but I don't want to cause a fight before the work week again.
I feel asking is better than snooping, but if he knows I'm going to want proof he's keeping his word he will delete things.
He says he wants us to have a trusting relationship that I am having to prove to him that I will be a happier more positive person I've begun therapy and am trying very hard. These urges or feelings are really bringing me down though. I feel if I ask and if I get rejected I will be more upset and suspicious and try to snoop. If there is an issue I know I should just end things. This is the biggest issue I have and only issue I have in this relationship. So I do not know what to do. It has been eating me up inside for at least 4 days now.
Any suggestions? Possible scenarios and outcomes and responses to it?

Daycia