Can you store a dirt bike in a shed?

any shed . if possible insulate the shed to help keep out moisture.  Dont just let it sit there. Start it once a week and fully warm it up. Clean it to as dust settles on it. Dont just stick it in the shed for winter and leave it there. Does it have a battery? Hook up a battery tender! I have bikes stored outside on my porch all year . Only one is a daily rider. the others are every now and then riders. More of them in my back yard under motorcycle covers. I just keep them gassed up. Start them ride them around the block . No issues happen . About to get another one LOL! 

Cant really stop rust. Can slow it by making sure no roof  leaks, drafts, and groundwater or rain flows  around it (a  ditch),

Might use a small electric  space heater at times (not the type with Glowing element, no. Solid state). 

  What Idiot said "stainless steel"?  It is chrome plated Steel, Steel, Iron, and aluminum (aluminium). Only  a Few  fasteners on my Harley are SS.  I Changed  'em.

The best place you can store your dirt bikes is without a doubt your home or garage. ... In short, as long as your dirt bike is in a closed place that no one can damage the bike, it means the bike is in a good and safe place.

My 4 bikes were stored under the veranda which was dry.  Winter weather is DRY if it is snow and ice...all liquid rain is frozen.  Bikes are painted or made out of aluminum or stainless steel so rust is not a deal.  If you really wanted to make sure you can coat the front forks in a thin coat of motor oil and they are good for the winter.  Dirt bikes are driven in the mud so they don't rust up.  I use a water hose to hose the mud off the bike and it dries in the sun.  They don't rust.

You can certainly store it in a shed if you like, beats storing it outside.  Ideally, a shed should be lockable, rodent proof, have a floor that blocks ground moisture, and be insulated, because slowing the rate of change in interior temperature will reduce the tendency for condensation and rust to form. If you can run a dehumidifier in it, you will drastically reduce this risk of rusting.  The manufacturer will have a list of things that need to be done for seasonal storage, such as doing a thorough cleaning, using a fuel stabilizer, replacing all fluids, etc.  A proper cover for the bike will be breathable and keep your bike clean for when spring arrives.

You can, but I wouldn't personally.

A shed with plenty of security. Stealing dirt bikes is a big industry.

Any shed that does not leak should be fine.  Also - inside the shed - still cover the bike with a tarp.

I live in an area with heavy winter snow and spring rain and many people in my area will store motorcycles or dirt bikes in sheds (usually covered with a tarp for extra protection) and they don't have any issues with the bike.  A heated space is not required.  Cold temps don't matter as long as the bike stays dry.