I have off-white rayon ribbon that I dye with Distress Inks ~ it just comes out wrinkled after I dye it.
How I dye it ~
*I pounce some ink on my non-stick craft mat.
*Add a couple squirts of water to the ink.
*Wad up the ribbon and rub the ribbon around in the ink.
NOTE: Wadding the ribbon up makes the dye job a bit uneven to add to the vintage look.
*Repeat with a 2nd or 3rd color if desired.
*Leave the ribbon wadded up and either let it dry naturally or hit it with the heat gun to speed drying.
Works like a charm and only takes a minute or so for the whole process.
Here is a banner I made ~ the ribbon was made as described ~
Ink Stains Banner & Rayon Ribbon.