Is it true that reading in bed makes your eyes bad?

Not at all. Neither is there truth to the myth that reading in the dark or sitting too closee to the television will damage your eyes. The eyes are essentially solid-state video cameras, and cannot be damaged by dim light, uncomfortable reading distance or anything short of trauma. Of course, reading with good lighting is more comfortable and enjoyable!
No. Read all you want in bed, just get the distance comfortable and have adequate lighting.