To dispose of old bedding you can simply place the old bedding with your regular garbage pick up if your garbage collector takes the old bedding.
If not you can take the old bedding to a recycling center or dump to dispose of or pay someone to haul it off if needed.
When mattresses arrive at the dump the mattresses are often just pushed into a pile with the other garbage and then buried where it rill remain until it rots away and the springs rust away from the mattress.
Some dumps may have recycling programs for the old mattresses, but the majority of dumps just bury the old mattresses, box springs and other bedding along with the other garbage.
In some places you may need to take old mattresses, mattress box springs and mattress toppers to the dump yourself or to a larger dumpster if your town has one.
Many local recycling centers also accept old mattress toppers for recycling and some companies offer recycling programs as well for mattresses and mattress toppers.
Some people also collect old mattresses and box springs to recycle the materials and reuse the materials in the mattresses.
Mattresses contain materials that can be used as insulation such as in dog houses and the springs in the mattresses can also be recycled for metal.
Some people also use the old mattress materials as bedding for dogs and other pets.
Box springs also contain wood which can also be reused in making things including dog houses.
I collected a few old mattresses off the curb before and used the material as insulation for a dog house.
Then I used the wood from the box spring or bottom part of the mattress to make the dog house for my dog.
The foam, steel coils and fibers from a mattress can be reused and repurposed and recycled into new products.
Many people just simply throw the mattresses and box springs out when they no longer need them which is okay as well if you don't have any way to recycle them.
A prison close to where I live also takes and collects old mattresses and box springs to recycle into materials for dog bedding and dog houses and they then send the coil springs off to a metal recycling scrap yard.
The trusted inmates come out to help unload them in a designated area.