Does the Bleach anime stick to the manga's plot? Does the anime series of Bleach stick to the manga's plot? Or is it like the original Fullmetal Alchemist series where the anime is its own thing and doesn't follow the story of the manga?
The anime pretty much stick to the manga, except of course during the filler arcs. The filler arcs are the Bounto Arc, Third Squad New Captain Amagai Shuusuke, Zanpakutou Rebellion, and the Gotei 13 Invading Army arc. There are also occasionally filler episodes among the canon arcs. A detailed comparison is available on Bleach Wiki.