Do bed bug live in covers?

Assuming you are referencing blankets or comforters, the answer is yes. If the items are not laundered regularly, Bedbugs will take harborage in the seams and creases of these items. It is not as favorable a spot at the actual mattress, box spring, bed frame and/or headboard because these items usually remain motionless while bed coverings get moved a lot especially while you sleep but I have seen Bedbugs living on them.