How do you properly store tubers?

[Bulbopedilum]

I have 4 pecteilis susannae tubers which I have unpotted. I unpotted them because if I leave them in the pot outside, chickens might wander and find them or stray cats might knock over the pot and make the tuber roll away.

I am currently storing them in a plastic bag in a plastic container (so ants won't get to them) in a drawer, but I was wondering if there is a better way to do this. Can you store them in a fridge? (This is a hot-growing species so Im not sure.)

Will fungus come if I continue to store the tubers like I currently am?

They will be stored for about 5 months, but what about if I want to store tubers for longer?

Thanks!