Bears hibernate in spans of a few weeks to several months, depending on the species, the weather, and available food stores. During that period, their metabolism drops to about a third of normal. There is a shift away from protein and carbohydrate metabolism toward fat breakdown. These processes result in a few notable changes in renal function: creatinine rises (from an average of 1-1.5 mg/dL to 3 mg/dL, thought to be due to decreased renal perfusion), and urea:creatinine ratio falls (as a result of decreased protein metabolism). A small amount of urine, about 100 mL, is produced, and the water and nitrogenous breakdown products are reabsorbed through the bladder. How does this happen? No idea. Urea is degraded, again by an unknown mechanism: one theory is that urease-producing bacteria in the gut aid in breakdown. Nitrogen is also thought to be shunted toward protein anabolism. The amazing result is that blood from hibernating bears does not contain an elevated level of urea, uric acid, amino acids, or ammonia. They replenish the water lost via respiration via lipolysis, where water is an end product. Interestingly, despite increased fat metabolism, bears do not develop a ketosis. Again, not sure why (may be related to increased glycerol metabolism).
So, next time you see a bear foraging through garbage pails, or sniffing around your campsite, remember: he may be looking for food, but he does not need to find the latrine.