How to insulate a bedroom over a laundry and furnace room.

If the floor is where you think the cold/heat is coming from- insulate the ceiling in the basement. If it's the walls, insulation can be blown in from the attic or holes drilled in the walls. If you don't want to blow insulation, use heavy drapes on all the walls. Drapes will really help. If you can't insulate the ceiling in the basement, buy throw rugs.

if you are insulating from sound there are grey nubby square acoustical panels you can get. if the basement is unfinished staple them in place from below.

There are also sound deadening batting and rigid panels to sound-proof an area..... https://www.homedepot.com/p/Roxul-Safe-n-Sound-3-in-x-15-1-4-in-x-47-in-Soundproofing-Stone-Wool-Insulation-1-Batt-RXSS31525/202531875

If you have access I would spray foam insulate this will cover sound and moisture

Spray foam is a really good option

i wish i had your problem. i can set the thermostat to 68 and have the bedrooms at 55 degree

I'd buy the most dense rolls you can afford. And then put aluminum backed foam board over that. The aluminum should face the floor of the basement. If the aluminum backed board is too expensive for you, buy just the foam board and glue heavy duty cooking aluminum on the board. Shiny side should face the basement floor. Good luck.