Alrighty! I’m home now and have FOTR open before me, and the Baskii DVD playing. (and if this isn’t total geek immersion, I don’t know what is!)
Now that I look at it, I see there are actually two scenes in the book that are conflated to inspire the scene as it appears in both films. Both are in “Three is Company,” a few pages apart.
The first is a few paragraphs after Frodo recites “The Road goes ever on and on…” He, Sam, and Pippin are walking along the road in the woods, when they hear a horse approaching; it could be Gandalf–or maybe not. At Frodo’s advice, they get off the road; Sam and Pippin “ran quickly to the left and down into a little hollow not far from the road.” Frodo lingers `til the sound of the hooves gets closer, then “threw himself down in a patch of long grass behind a tree that overshadowed the road Then he lifted his head and peered cautiously above one of the tree roots.”
When the Rider comes up, he pauses on the road above Frodo and sniffles, but does not get off his horse. Frodo feels a desire to take the Ring out of his pocket, but doesn’t. And then the Rider passes on.
A few pages later, after the hobbits have gone on awhile and it’s now night, they hear footsteps again. (You can find this just after the long song that starts “Upon the hearth the fire is red…” ). This time, Sam and Pippin crouch behind a “large tree bole” (bole = trunk, not roots) and Frodo “crept a few yards back toward the lane.” The Rider arrives leading his horse, and gets down to sniff along the road; as the Rider gets close to him, Frodo feels an even stronger desire to put the Ring on, but just as he reaches for his pocket, the Elves show up and the Rider retreats.
So, I can see the elements of the scene as it plays in both films: Frodo peeking out from the tree roots with the Rider above him, for example, and the Rider later crouching down on the road. But there is no point where all 3 hobbits hide under a tree root together as they do in both movies (and never mind the films’ addition of Merry, since both versions change how the hobbits start out anyway). Unless there is some illustration that inspired both, I’m going to stick with my original contention that Jackson’s scene is an homage to Bashki’s.
As for the ending of Bashki’s film, Gandalf throws his sword in the air, and the narrator proclaims: “The forces of darkness were driven forever from the face of Middle-earth by the valiant friends of Frodo. As their gallant battle ended, so too ends the first great tale of The Lord of the Rings.”
Which does suggest a sequel, although one has to wonder how important Frodo’s quest is now that “the forces of darkness were driven forever from the face of Middle-earth.”