Yes, you can catch the shiny version of Tapu Bulu in Pokemon GO, but only if you are very fortunate.
The exact odds of catching shiny Legendary Pokemon in Pokemon GO is 5%, meaning, on average, you will only find 1 shiny Tapu Bulu for every 20 times you encounter one.
The best time to catch the shiny version of this Legendary Pokemon is during the Pokemon GO Tapu Bulu Raid Hour. This is because the number 5-Star Raids featuring this Pokemon will be greatly increased then.
Of course, shiny Tapu Bulu will also be available to catch whenever it is a Tier 5 Raid boss. This is following its shiny version being added to the game on April 17, 2023.

What Color is Shiny Tapu Bulu in Pokemon GO?
The shiny version of Tapu Bulu is mostly black and has light yellow horns, hands, and tail. It also has white markings on its body.
The main difference between the normal and shiny versions is that all of the red parts of the normal Tapu Bulu turn black for its shiny. However, the yellow color of the standard version turns lighter for the shiny one too.
This color scheme is also the same as the other Legendary Tapus from the Alola region. Both shiny Tapu Lele and shiny Tapu Koko also have a primarily black and white color scheme.

Shiny hunters have dozens of Legendary shinies to catch in Pokemon GO, and the list keeps growing! Find out every shiny Legendary Pokemon in Pokemon GO so you know which ones you still have to catch!