Leave the boyfriend to one side of this thread for now.
DS did this, at about the same age. It was after we left Egypt, and were staying at my mums. DS doesn't do change all that well, he accepts it, but doesn't like it.
He used to creep in with me, and for a quiet life, and I was in a King sized bed, so he didn't disturb me I let him do it for a while, but told him that his bed was his bed and mine was mine.
We moved to a rental house and again he did the same. I told him that he couldn't sneak in with me during the week and if he did, I would take him back to his room, tears or no tears, as he had nursery the next day and needed to sleep properly.
There were a couple of times I had to walk him back, telling him that I loved him, but that we both needed to sleep properly as we had school in the morning.
Important to be consistent and strong here!!
Then I told him that it was time he slept in his bed and me in mine, all night, he accepted it.
dmd34, your DS more than likely IS reacting to the new man in your life. He needs reassurance, if letting him stay for a night or 2 a week is not an option, then you are going to have to be strong, and take him back to his bed every time. Talk to him about it before he goes to bed, explain what you expect of him.
Now to the BF... you need to sit him calmly down and explain that this is a tricky time for ds, his age, the new man in his mum's life, but that you are aware of the issues of the sneaking into bed and will put a stop to it. HOWEVER that he is your son, and therefore you need to lead this process and he, the BF, must be more understanding. It's difficult for a 4yo to understand all of this, and it's your job to help him, and the BF job to back you up and support this process for as long as it takes.
He still is a little boy, he just needs a little help to get through this.
FWIW, the more he supports you and backs your position and is patient with your ds, the faster your ds will be able to get over this.
If your BF makes a fuss about this, tbh better to tell him to sling his hook, cos he is on the borderline of overstepping the mark. We all know it doesn't get any better when they move in.... only worse, so if he is taking this all badly, it's a pale red flag for me.