I’ve used the worsted weight silk roving in a pair of mitts, and in a pair of slippers, and both have been plenty sturdy. I haven’t had issues with those bleeding, but I also haven’t washed them. Remember that the yarn was washed during the dyeing process, so most of the stray dye has already been washed out. Beyond that, if you’re worried about color bleed, put the hat in a bowl of lukewarm (not hot) water, with a drop or two of gentle detergent, or even Dawn if you don’t have a gentle laundry detergent around. Then after it soaks a bit, gently squeeze out the hat (just a bit), then wrap it in a bit of paper towel, inside an old cloth towel. The paper towel will show you any color bleed, and the cloth towel will absorb most of the water. Then just let the hat dry on a rack.
Hand washing gets a bad rap, but it really isn’t hard, and only takes a minute or two, and lets you keep precious handmade things in good condition. I’d go for it if I were you. Especially since something like a hat doesn’t need to be washed often.
Meanwhile I’m considering turning my two cakes of Phenomena into a sweater for a tiny human. I have some of the worsted weight sparkle in blue that I think would make a great edging paired with the multi colored Phenomena.