[MozartLover]

Well, as Frodo was running down the path and shouting for help, he became aware of Tom's presence far behind him, not in front of him where it would have been easier to hear. Also, Frodo could barely hear himself because of the effects of the willow-wind. Tom was clearly returning from somewhere as he states in his song ("Old Tom Bobadil water-liles bringing Comes hopping home again. Can you hear him singing")? So it would appear, at least, that he happened upon the scene........

[JenB]

Tom was fetching water-lilies for Goldberry, remember? The last of the season, to flower about her feet until spring. In fact he said he would not be going down that path again until spring, so it was both coincidence and not - they said they were watching for Frodo and company. (Um, I'm not sure if some of this is spoilers for the next chapter but you wanted to know!)

[sweetliberty]

"So it would appear, at least, that he happened upon the scene........"

Still, there seems an air of divine providence about it.