I would think carefully about using steel only. If your bed was designed to have a wood floor the cross members are say 18" apart? And if it were to have a thin steel top as you are looking at then I would guess somewhere around 8 to 12" is a better spacing for the cross members. If you set something heavy that lands between the cross members and has a point load, like a heavy desk, or a machine tool with feet, then the steel will not stay flat for long.
Do you have any pictures of the bed and how it is constructed?
I would recommend white oak as a nice looking, strong, long lasting, and reasonably cheep floor.
Grigg