Bog Lord Tendrils are pieces of fungal giants that can be collected after killing them. The Sporelings of Sporeggar accept them as proof of your thinning their numbers.
There are three places to grind Bog Lord Tendrils.
Dead Mire, off Withered Bog Lords and Withered Giants: The traditional mating ground of the giants has plenty of the creatures around to kill. There are Parched Hydras lurking about as well, but they can be easily avoided or killed while waiting for respawns. In addition, the mobs here are lower level than in other areas, so everything is easier to kill. While the Dead Mire is the location of several Horde and Alliance quests, competition generally is fairly low, as the area is large and the mobs plentiful. If a PvP war is raging, however, the open nature of the area makes hiding impossible, and rezzing a pain.
Spawning Glen, off Starving Fungal Giants and Starving Bog Lords: For grinding Sporeggar rep, you won't find a better place then here. You can kill plentiful giants and gather Mature Spore Sacs all at the same time. This, of course, draws a great many players to the area, unfortunately, and so competition is high. Conflict can be avoided easier than in the Dead Mire, however, due to the readily available cover.