There are lots of old "theories" circulating about just what in the urine causes the killing off of your prized Bermuda grass. The most common of these misguided opinions is that the urine is acidic and 'burns' the grass. As a result, a host of home remedies have arisen to change the pH of the urine. These measures rarely work because the real culprit in urine burns is nitrogen.
Because dogs are carnivores and eat a high level of protein in their diet, they break the protein down and excrete it as nitrogen in the urine. The result is a killing of the grass from an overload of nitrogen. You will get the same kind of burn if you put a concentrated handful of fertilizer in one spot. These urine burns will often have a characteristic green ring around the outside edge where the urine was dilute enough to actually work as a fertilizer. This characteristic ring can also help distinguish urine burns from a grub infestation that will also create similarly looking brown spots.
There are a few things that make urine burns more prevalent: