Real wood (not plywood etc.) should be ok, as long as you're not using something aromatic like pine. You can always off gas it in the garage or somewhere not in your house, for a month or however long it takes, to make it safe to bring inside.
You could also buy a used bedframe, assuming the previous owner didn't pour perfume all over it or something. This would have the advantage of it already being off gassed.
You can also seal the wood with American Formulating and Manufacturing (AFM) sealer to seal off any off gassing.