The western and central parts of today's Indonesia had Hindu/Buddhist kingdoms since at least the 4th century. Kingdoms such as Srivijaya (a Buddhist maritime kingdom based off the Malay peninsula, Sumatra, and parts of Java), Kediri (a Hindu kingdom mostly in central Java), Singhasari (its larger successor), and finally Majapahit (a Hindu kingdom centered on Java). While the existence of these kingdoms are known both from local and foreign sources (Chinese and Indian chronicles), the extent of their powers are largely unknown and is debated today.
Islam entered into the western and central parts of Java during the decline of Majapahit in the 14th century. The fall of Demak to an Islamic rival prompted Hindu courtiers, nobles, priests, to move to Bali in the 1500s. Not long after, the Portuguese started to enter the archipelago in the 1580s, changing the balance of power dramatically. As a result, the newly founded independent Kingdom of Bali was not conquered by Islamic powers in Java.
As the Dutch VOC displaced the Portuguese in most parts of the archipelago, they remained mostly on the coasts, content to control the maritime trade of their desired commodities. As such, there was little interest in Bali, which mostly kept to itself and had no desirable commodities.
In the 19th century, the Dutch colonial government started to push inland to directly control areas they previously didn't want to. Over time, they conquered the now-fragmented kingdoms of Bali until in 1908 they completed the subjugation.
So in short, the arrival of Europeans upset the process of conquest by Islamic kingdoms, and the disinterest of European entities left Bali alone until the 19th century.