Dye catchers are worth their weight in gold. I think the one I use is made by Shout, terry-clothish, and good for 30 loads. Batiks definately shed some dye.you can use the search feature on the top of the page to find some discussions and reviews.
Regarding clothes line or dryer, a dryer should further shrink the fabric. As to ravelling, there are a few threads here about that. pinking and edge zig-zagging work for some. For small pieces, I like using a lingerie bag.