moving stuff out to a shed

Aye no doubt they will be packed up in a nice warm place then shifted out to the cold shed. Instant condensation in the "sealed" bags, not a good idea.

Probably be OK for a short term, a few weeks at most, but anything longer really needs somewhere better than a cold, damp, unheated, shed.

I'd be more worried about vermin.

MBQ

No friends or family that will look after them? No self storage places nearby? I have even known people store stuff under the desk at work.

There's no way would I put any of my books oout in a shed.

MBQ

It would indeed be a good idea to deploy a mousetrap or two. Just make sure that they are in a place where the mice are likely to find them before they find the books.

Mice can be terribly destructive - especially if they decide take up residence, and start building a nest. They are regular visitors to my garage (where I have three traps set) but, surprisingly, they usually seem to ignore the sheds. In principle, I don't believe in killing them (or any other creature), but I think I can honestly claim that it is in self-defence.

Something vermin proof, which a bag isn't

Aldi have a special offer on vacuum bags on Sunday, may be worth a look.