I would like to think that the brontasurus was the animal that the bible writer was describing as it appears to talk about a very large powerful animal, particularly when it describes his tail swaying like a tree (cedar).
Since there were no living dinosaurs in the ANE, and there hadn't been for 65 million years, it is particularly unlikely that this would have been the case. Also Apatosaurus did not live in the region; its fossils are found only in North America.
If the Israelites and other ancients really lived alongside such a creature, not only would there have been bones but there should at least be other references to it, or even a word referring to it. There is no name for this beast; "Behemoth" is simply the par excellance word for "wild beast".
And FWIW, (1) The Behemoth is described as eating grass. Apatosaurus did not eat grass (which did not exist in its day), it ate leaves. Grazing animals eat grass, and so the Behemoth is compared to one. All ruminating animals have molar-like teeth for chewing grass, Apatosaurus did not have any teeth for chewing, it swallowed leaves whole. And it was built to forage treetops like a giraffe, not grass on the ground. (2) The Behemoth is described as hidden in the shade of the lotus plants near the water, or covered by reeds only several feet tall. This is hardly the image of a huge Apatosaurus. (3) Similarly the Jordan is described as rushing to its mouth when it rages. The Jordan has a depth averaging 6-10 feet whereas the Apatosaurus was over 30 feet tall; again the Apatosaurus is too big. (4) As for the reference to the cedar-like tail, it is widely accepted that the "tail" is a euphemism for the animal's erect penis; this is particularly apparent since the preceding verse referred to the creature's loins and the stiff cedar-like tail is in poetic parallelism with the tendons of the animal's "stones" (a euphemism for testicles, cf. Leviticus 21:20). Dinosaurs probably didn't have external genitalia but rather cloacae.