I'm weird, but my initial thought to your original post was when you mentioned having a bed in the room, and then asking about dampening .. a bed may already provide pretty efficient sound dampening

One thing I learned in my house (YMMV) .. if you don't like the sound of the mic where you have it right now, move it and try again
I've found trying things like (instead of a closet) put the mic in a hallway .. doesn't sound *quite right? turn it around and face the other end of the hallway .. open/close different doors in the hallway .. ended up with some pretty decent vocal tracks that way

All that typing to say -
Experiment and figure out where/how your space can work for you, that's a pretty cheap option to try first before investing in other stuff and then figuring out how to use that other stuff

I do not work here, but the benefits are still awesome
Make your sound your own!