Urine exits the kidney drop by drop as it is formed and is only stored/collected in the bladder. That is why there is progressing filling of the bladder other than a sudden situation.

Before exiting the kidney, into the bladder, via tubes called "ureters," fluid collects in the kidney in tubes, or "tubules." In these tubules, blood is filtered, and extra water and waste pass as primary urine. In the tubules, filtered solutes and water return to the bloodstream, during reabsorption, leaving the waste products concentrated in a solution that becomes urine.