What might be causing discoloration of my bed-ridden Mother's skin?

Hard to say without seeing it. Many elderly people have skin discolorations especially on their arms and hands. If she's picking at it she could get an infection. Try some antibiotic ointment with a 4x4 dressing and wrap it (not too tight) with a rubber bandage (like a rubbery band aid that goes around the arm and looks like an ace bandage). This rubber bandage might help your mom from picking at it . Check it everyday, see if it's healing.