Just so, why did Bruce Wayne leave Gotham City?
In 2015, Bruce left Gotham after killing the Joker, leading the local crime rate to rise higher than ever and the Bat-Signal to be finally switched off in 2018 to signify his permanent absence. After discovering his secret identity, Kate took on her cousin's mantle and became Batwoman.
Furthermore, is Batman good or bad for Gotham City? Yes, Batman is making Gotham better. Despite what other answers have claimed, there is NO EVIDENCE that crime or corruption have gotten measurably worse since Batman arrived.
One may also ask, why does Batman disappear?
Batman disappears by taking advantage of human nature and human assumptions about what is possible the same way a stage magician might. Batman's ability to disappear is more a skill of misdirection than of supernatural capacity.
Where did Bruce go when he left Gotham?
He left to train. In Comics Bruce Wayne travelled the world for years and had a lot of martial arts training before becoming a crimefighter.