Mammalian bladders presumably evolved from the bladders of mammal-like reptiles.

The bladders of mammal-like reptiles presumably evolved from the bladders of amphibians, no doubt via a few transitional forms.

Amphibians, even aquatic amphibians, have bladders. Aquatic amphibians use their bladders mainly as part of their system of osmotic control. Terrestrial amphibians, particularly those in arid areas, also use their very large bladders for storage of water. Some of their Permian descendants, during the period in which adaptation for survival and reproduction away from liquid water became crucial, evolved the uric acid route of nitrogen excretion. They gave rise to the modern reptiles and birds for example, while others, in particular the mammal-like reptiles, evolved the more water extravagant urea route and retained comparatively large, functional bladders. They certainly had no need to develop bladders from scratch, though they did need to adapt their bladder physiology for mammalian requirements rather than amphibian requirements.

As a matter of fact, some mammals, including some voles and mice, do piddle more or less continuously wherever they go. No doubt the benefit, apart from physiological simplification, is one's personal identification, and territorial marking. Interestingly however, apart from such piddle trails being helpful to weasels and the like, they are very visible in ultraviolet, and some birds of prey, such as kestrels, can see in ultraviolet and use the signals for vole hunting.

As for "What use is half a bladder?", That depends on who you are. If you are an aquatic amphibian, it is very useful for osmotic control. Other uses could develop under the selection pressures arising from new ecologies.

Good enough, I would say.

Cheers,Jon