Cole in Leicester sell large rolls of ribbon very cheaply.
Cole Fabrics - Welcome - Part of the Global Ribbons Group
I have a 200m roll of double satin ribbon made from polyester that can be dye sublimated onto.
I'm not sure what type of ink you would need to use for screening onto them, I would be interested in this. I've tried pad printing them with the solvent based ink we use to print pens / lighters and it washes off in the first wash.
Sublimation onto this material works perfectly but it's a clumsy process and the ribbon stretches (or shrinks - i cant remember) during the heat press stage.