You might be in a bit of luck because one of the Bulbmin caves is the Submerged Castle (AKA the Waterwraith's haunt). Admittedly, it's the only good part about that level (especially since you're only allowed to bring Blue Pikmin in unless you use some kind of glitch or skill to bring other colors in there).
Besides that level, they also appear in the Frontier Cavern (in the Valley of Repose) and the Hole of Heroes (in the Wistful Wilds).
Besides that level, they also appear in the Frontier Cavern (in the Valley of Repose) and the Hole of Heroes (in the Wistful Wilds).