If I knew the wall adjoining the kitchen, I might suggest a simple and inexpensive solution. Is it a solid, unbroken space and can the headboard be placed on it? If so, why not insulate with batting under drape or upholstery along the entire wall with the headboard centered on it? Should do the trick and add some style and softness to the room.

Forgot... search at the top of the page for "upholstered walls" or "fabric walls" and such for ideas.

Ask you contractor about expandable spray foam insulation. It offers better sound proofing than conventional fiberglass insulation.

Can you put the head of the bed on an non-adjoining wall?

Usually there is a physical break in the walls - an air space so the vibrations do not travel.

Search the internet for images and discussions on soundproofing, like this: http://www.google.com/imgres?imgurl=http://www.soundproofing101.com/images/soundproofing_wall_new_construction_graphic.jpg&imgrefurl=http://www.soundproofing101.com/soundproofing_3.htm&h=420&w=451&sz=15&tbnid=ioaJTVBzVl8E5M:&tbnh=90&tbnw=97&prev=/search%3Fq%3Dsoundproof%2Bwall%26tbm%3Disch%26tbo%3Du&zoom=1&q=soundproof+wall&usg=__8s9wqrP2xGenr68aluCWfzEoyKU=&sa=X&ei=EKk7UMiTO47H6AGuyIHgBA&ved=0CEUQ9QEwAA&dur=9719

I'm assuming we are talking new construction. If you have not framed the wall yet, there is a special framing technique for sound deadening that your framer will know. Basically, within the wall, the studds for the two walls are staggered and studded independently. Spray foam would be best, but there is also certain sound deadening insulation in roll form. There is also sound deadening drywall, (I think it has a metal mesh in it ) that you can special order. It won't be too expensive and you only need it on that wall. None of this, (except for the spray foam) will be very expensive or increase your costs too much.

We recently put an addition on our house and used "Roxul Safe'n'Sound" insulation in all interior walls between new b.r., bathrooms, laundry room. http://www.roxul.com/residential/products/roxul+safe%27n%27sound%E2%84%A2 Easy to install, my boyfriend did it himself, but it can make exposed skin a little itchy if not careful. He had it installed in no time. Purchased at Home Depot.