Anytime after defeating the Pokemon League, 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 for Pokemon on the ground.
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 you possibly can. Steel Type Pokemon are best against Bulu, especially since its move don't do that much damage to them. Having False Swipe as a move on one of your Pokemon also helps, since it will guarantee Tapu Bulu is left with at least one HP. If you have the Rotom Power that makes it easier to catch a Wild Pokemon, then you should definitely consider using it here as well.
From there, after getting its HP as low as you think you can, Ultra Balls are the best way to capture 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.