Just considering the weather, the cooler dry season from April to October is the best time to visit Bali. The rest of the year is more humid, more cloudy and has more rainstorms, but you can still enjoy a holiday.
There are also distinct tourist seasons which affect the picture. The European summer holidays bring the biggest crowds - July, August and early September are busy. Accommodation can be tight in these months and prices are higher. From Christmas until the end of January, airfares to/from Australia are higher and flights can be booked solid. Many Indonesians also visit Bali around Christmas. Outside these times Bali has surprisingly few tourists and there are plenty of empty hotel rooms and free tables in restaurants.
Balinese festivals, holidays and special celebrations occur all the time, so don't worry about timing your visit to coincide with local events. Just make some inquiries when you arrive and be prepared to travel around the island.