It doesn't take a miracle for a 4 month old to sleep through the night. They should be.
When my babies were little, they slept in a bassinet by my bed, too. And they both went through stages where they just wanted human contact, to know that I was still there. If they can't see of touch you, you might as well have abandoned them on a rainy doorstep!
So I would hang my arm into their bassinet and keep my hand on their tummy. Sounds too simple, but they'd relax and fall asleep within a few minutes. My arm usually went numb because the edge of the bassinet was higher than my mattress, but it was worth being able to sleep!
I've got a little one coming soon, and now my bed is on risers, so hopefully that arm-numbing thing will be better this time. If not, I think I'll take the wheels off the bottom of the bassinet to lower it a an inch or two.
Good luck!