Unfortunately, there's really nothing you can do to prevent your mother from bruising easily. This is a normal side effect of having a low platelet count, which means blood doesn't clot as easily. Cancer patients with low platelets get severe bruises, and sometimes they don't even know how they got them. What you can do is change her environment and habits to try to minimize her chances of bumping or injuring herself. I always have my patients rearrange their rooms to make clear, wide paths from one place to another so they don't bump into furniture. You may even want to move a few pieces of furniture -- particularly those with sharp corners -- out of the rooms your mother uses.
Have her wear shoes or slippers at all times, indoors as well as out, to prevent stubbing her toes or bumping her feet. Avoid anything tight or elastic whenever possible -- I've seen patients bruise from blood pressure cuffs, for example. Make sure the elastic in waistbands and socks isn't too tight.
I counsel patients not to feel like they're made of glass and compromise their quality of life too much. If your mother loves to garden or walk the dog, she shouldn't give that up, even if it can contribute to bruising. Maybe someone else can walk with her and hold the leash if the dog tends to pull, or she could wear gloves to protect her hands.
If your mother's platelet count seems to be staying very low and not improving, this is something you want to let the doctor know about. Every lab has its own reference range for normal, so I can't give you an exact number, but you want to look at your mother's lab tests and make sure she's not too far outside the indicated range. If your mother's platelet count drops dangerously low, her doctor will order a platelet transfusion.