I have never gotten a t-shirt signed by the characters but I have several that are signed by local band members. They are all plan cotton t-shirts in solid colours. I used a Sharpie as well and I wear them regularly so I wash them just like I would any other shirt. I have never once had a problem with anything bleeding and I've owned a couple for a very long time. I do make a habit of turning all of my clothes inside out when I wash them. Maybe this had something to do with keeping their good condition. Also, I wash anything like that in cold water, never warm or hot. Hope this is helpful.
Ali