Anytime after defeating the Elite Four and the main storyline, you can Battle Tapu Bulu, the Island Guardian of Ula'ula, at the end of the Ruins of Abundance. Like Tapu Koko and Tapu Lele, it will also be at Level 60. It's ability instantly creates a Grassy Terrain, which boosts Grass Type Attacks and allows for HP recovery every turn.
Tips For Catching Tapu Bulu:
Thankfully, unlike Tapu Koko, Tapu Bulu actually can be paralyzed. This makes it much easier to catch and almost ensures your Pokemon will always move first. After paralyzing Tapu Bulu, try to get it's HP as low as possible. Steel Type Pokemon are best against Bulu, especially since its move don't do that much damage to them. Having False Swipe and Hold Back on some of your Pokemon also helps, since it will guarantee Tapu Bulu is left with at least one HP.
From there, after getting its HP as low as you think you can, Ultra Balls are the best way to capturing it. It will usually take a lot of them to catch this Legendary Pokemon, but they are still your best option. And don't forget to save before battling Tapu Bulu, just in case you are going for a certain ability or accidentally knock it out.