I have some Touch Twin and also Copics, Bics and Sharpies. I use a cardstock similar to GP that I get at Sam's Club.
I tried the Memento ink, which is highly recommended by everyone who uses markers. I did not like that it doesn't stamp a really clear image, like the Versafine Onyx that I always use for stamping my images.
Anyway, the Memento did not seem to make a difference in the "bleeding" you are talking about, so I went back to my tried and true Versafine.
This is just my way of coloring with markers, and maybe others do it differently.
I've found that ANY ink that I use will smear slightly if I actually color over the line with the markers. When I use markers, I am a very careful colorer, lol, and just color right up to the lines in the image, and try not to color over the lines.
It's kind of tedious, but I get the best results that way.
Here's a link to a card in my gallery that I colored using this method. As you can see, I don't do elaborate shading, but I like the results I get and that's okay with me.
Howdy Cowboy! by buggainok - Cards and Paper Crafts at Splitcoaststampers