I gave up on the water based dyes, however, I think if you try sealing with one of the acrylic based products you may get better results. You can try Resolene. Take a sponge, wet it, and wring it out. Apply a very small amount of Resolene to the sponge and wipe very lightly in one direction on your belt. If you can see a milky appearance, you are applying it too heavily (make another very light pass with the sponge to even it out). Allow that to dry and apply another very light coat. I apply 3 or 4 coats in this manner and have ended up with a very nice finish. After the first or maybe the second coat, you should not see any more dye rubbing off.The key here is patience. Use very light coats of Resolene, very light pressure, and let it dry well. Some folks dilute the Resolene, but I use it full strength. Also, a lot of folks on here airbrush their finishes which I understand works very well. I just don't have the room for that kind of setup.
I hope this helps.