The Bladder is one of the six fu, the hollow yang organs, and is paired with the Kidney in the Water phase. The fu are defined by their common function: they receive, transform and pass on, and unlike the zang they are described as filling and emptying rather than storing.
What Chinese medicine says the Bladder does is close to the western account and then extends past it. It receives the fluid the other organs have finished with and holds it until it is voided, which is unremarkable. The extension is that this is described as a qi transformation, dependent on the Kidney's yang, so that the tradition treats the Bladder's function as an expression of the Kidney's condition rather than as independent of it. Fu organs in this system are generally described in terms of the zang they pair with, and the Bladder is the clearest case.
Its channel is the longest in the body and carries the row of transport points that index all twelve organs, which gives the Bladder a prominence in practice out of all proportion to the function described here. That is treated on the Meridian's own page rather than this one.
The atlas records the western placement of the bladder under Scorpio in a separate article. Neither account asserts anything about urinary physiology, and nothing here is medical guidance.