Time and time again I'm called out publically on why I advocate using baking soda to neutralize my rust dyed fabrics! Here's my "edited response"
... rinse in baking soda solution once a year [Edited] Synthropol does NOTHING to stop the rusting process! If you'd like to slow it down and I can certainly understand wanting to do so then neutralize it once a year with a baking soda solution! That is why I recommend this step is because you are neutralizing the acids on the fabrics surface.
In conservation if we want to stop or remove "foxing" which most would see as either a rust spot or something akin to a scorch mark then we neutralize the piece or area with a baking soda solution. First the piece is washed in a pH neutral soap and if that doesn't remove the spot and removal is necessary then we use baking soda solution. Foxing is typically caused by linens etc., that come into contact with high acid woods such as cedar, pine, oak, etc., when they are stored in hope chests, dresser drawers, etc.
Some of us, that would be me, are eagerly anticipating the deconstruction of our pieces due to the rusting and composting processes.
If your piece is not too heavily rusted then and you want it on your bed then I say go for it! Just remember that anything it comes into contact with may also start to rust over time.
Yes your rusted piece will continue to rust, and eventually holes may appear in the fabric. NOTE that this all depends on where you live as in how high your relative humidity is etc. Rusted fabric in say Louisana will have a much shorter life, due to the high humidity, than say rusted fabric that lives in Utah or Arizona where the humidity is around 20-30% year round.
You can slow down the rusting process, though you will never stop the process entirely, by neutralizing the fabric with a baking soda solution. You can apply the solution once or twice a year depending on where you live. Those of you living in the desert may never have to do this step.
I recommend 1 tablespoon of baking soda to 1 gallon warm water. Dissolve well and apply by either spritzing the fabric with the solution using a spray bottle or by direct immersion of the piece.