If you on top of that put on a puffy vest and trousers, even better. Again, they need to be synthetic, not down, I cannot stress this enough. You put on your puffy clothes on top of your wet gear and close them. I have slept with my boots on in the Army which is not nice. So instead, I put them in a stuff sack from my backpack, not watertight, and stuff them in the bottom of my sleeping back. Over my wet sock I put on my camp socks.
Now I am ready for bed, so I crawl into my sleeping bag and zip it to the top. It would be a big lie to tell you that this is a nice way to go to bed. But it does not take a long time to get warm, still wet but warm, and if you are tired enough, you do not care. The important part is to keep your sleeping bag closed all night even if it gets a bit warm: you do not want it to lose that pressure that is pushing the water out. I did this in New Zealand, five minutes after crossing a river with freezing water up to my chest. And I woke up the next morning and found my sleeping back soaked on the outside, but the inside and me being completely dry one the inside. If we are talking just damp clothing, you do not need to sleep in it, just sleep on in inside the sleeping back, or put it in the foot end. It will not dry as well as when you wear it, but it still works.
The thing I am telling you not to do. Back in my Army days, I heard whispers of a banned way to dry. Banned because people had burned themselves and gotten really sick from carbon monoxide poisoning. If you did however learn it, no higher up would tell you off for doing it, as they properly did it themselves. So, I am going to tell you how to do it, just so you can tell other people not to do it. And do not do it when you are really wet on a windy mountain side in New Zealand, looking for tahr on a cold August day. Because I have never done that, of course.
They call it the Finnish sauna, and what you need is a burner and tarp. You take the tarp and wrap it around you, as snuck as possible. If you a bit concerned about safety, make a small hole for your mouth to stick out. Then you light the burner between your feet. This will quickly warm up your small homemade sauna, and soon you will find yourself a lot drier. And once again, I have of course never been caught doing this, and as there are no photos, I have not done it.