Hello, my name isXXXXX and I have over 20 years of experience as a veterinarian.
I understand that you are concerned about Bandit urinating on the carpet and losing more hair then normal.
Shedding and inappropriate urination can be precipitated by stress, so it is possible that the two symptoms are linked. When stressed the body releases cortisol hormone which leads to loss of mature hairs from the coat, and stress can allow secondary infections to take hold or lead to a bout of interstitial cystitis.
Interstitial cystitis is a poorly understood inflammatory condition that causes thickening of the bladder wall, discomfort, a poor mucous layer on the bladder wall and bleeding of the bladder lining. It seems to worsen with stressful conditions.
Treatment options are varied although none seem to help all cats. I recommend medication to relieve stress such as amitriptylline or buspirone and feliway (a synthetic calming pheromone available at pet stores and online), an omega 3 fatty acid as well as a glucosamine supplement (both available from your veterinarian and at pet stores) as some studies show those decrease inflammation and improve the health of the mucous layer lining the bladder. Some veterinarians try steroids as well.
I also recommend increasing fluid intake as much as possible via canned diets, a kitty drinking fountain and offering low salt chicken broth or tuna juice to drink. See this link for a very good article from a respected veterinary researcher on interstitial cystitis: http://secure.aahanet.org/eweb/images/AAHAnet/phoenix2009proceedings/pdfs/01_scientific/103_UPDATES%20ON%20IDIOPATHIC_I.pdf
In some cats increasing play and positive interactions with housemates and their owners also seems to help. Playing more with Bandit, especially with interactive toys like fishing line things she can chase, laser pointers and toys she can retrieve seem to be favorites.
If she is an indoor only girl sometimes getting her safely outdoors helps. Most cats aren't thrilled with a leash but some owners build outdoor cat pens so that they can safely be outdoors. These can be built even on a balcony if you live in an apartment.
See this link for some examples:
You would think being an indoor cat and having no changes in her life that you are aware of, she wouldn't be stressed but cats are very sensitive. Things like outdoor animals and strays, especially during the warm months when they are louder and more active, changes in your work schedule or even extreme heat can be stressful.
It is also possible that she has a urinary tract infection, crystals or calculi in her urinary tract or an underlying metabolic disease process that has been developing and is now causing symptoms. I highly recommend a veterinary examination, urinalysis with culture and screening blood tests to make sure she is physically healthy.
If she is healthy then concentrating on finding the source of her stress and alleviating it if possible.
Best of luck with your girl, please let me know if you have any questions.