You can say that there are more visitors coming to Bali from April to October since this is the dry season. You probably think twice before coming to Bali in the wet season (October to April), at least you will think whether you are going to have bright days if you come on the wet season. If you would like to make sure that you will see no rain (at least 99.99% chance to see bright days) than you can choose to come to come during this time of the year.
There are few other things to consider. For example, the celebrations and local holidays.
The Silent day can take place on between March and April. Everything will be closed on that day that you will have to stay lock up in your hotel. June, July, and August is the busiest time in Bali because it is school holidays. The popular tourist areas are mostly flooded by tourists from our neighbouring island, Java. But there are also many visitors from Australia, Europe and Asia who come and bring their kids to enjoy the warmth of the sun in Bali.
There is another celebration in August: the independence day. You will see procession, carnival, and most popular is the kite festival held in Sanur. During this month you will see the Bali sky is covered with hundred of kites.
In the month of September and October the number of tourists has come back to normal because the holiday is over. We still have many visitor but not as much as the previous months. September is believed to be the best month since it has the lowest humidity but I am not quite sure about that since every day is hot and humid here.
Those are the things you can put into consideration when visiting Bali between April and October. In my opionion, it is best to visit Bali when it is not so many tourists around that you can enjoy more, especially if you like staying in Kuta. Other places like Nusa Dua and Ubud maybe not as crowded as Kuta. So, you can go those places instead.
Have a good holiday in Bali.