Prevent Sound from Entering Mattress through Bed Legs

Step 1: Prevent air transmission between the rooms. Sweeps for the door or a heavier door; look at the heating registers and windows; things like that. You're saying the sound is muffled, which implies the high frequencies aren't making it in, so I don't think this is the major problem.

Step 2: Damp the transmitted vibration. Put big heavy bookcases on the wall between the two rooms (which side doesn't matter so much). Blow heavy insulation into the wall between. Hang a heavy quilt on the wall.

Step 3: Break up the sound in the source room. Use natural diffusers (heavy sofas with heavy foam pillows work great, or the aforementioned bookcase with loads of stuff on it), or buy foam diffusers to stick in the corners/edges of the room.

Step 4: Give up and wear sound-cancellation headphones...or install a white-noise generator in your office (either a fan-type one, or a water feature if you like more 'natural' sounds).

See also How Do You Reduce Floor Sound Transmission for more details.

I fixed my metal bedframe by putting leather patches between parts that are rubbing. Wooden frame is a bit more tricky - not so easy to identify where the parts are rubbing, but this is the first initial step. I'd say check all the joints and see if you can tighten the bolts or add glue to moving parts.

Basically, the noise comes from parts rubbing on each other. If you can eliminate rubbing, or put something between the rubbing parts - that would reduce the noise.