Can't find anything on that song, but plenty about (Ed) the Bee Hunter. Several sites quote his supposed dying words:

     'But toom cam' the saddle, all bluidy to see,
     And hame came the steed, but hame never came he.'
  

which looks like a couplet from Bonny George Campbell.

However many of these seem to be based on Col. Crockett's Exploits and Adventures in Texas: Wherein Is Contained a Full Account of his Journey from Tennessee to the Red River and Natchitoches, and Thence across Texas. Philadelphia: 1836 by Richard Penn Smith. This was supposedly based on Crockett's diaries, but see COL. CROCKETT'S EXPLOITS AND ADVENTURES IN TEXAS: DEATH AND TRANSFIGURATION (pages 70..72 especially) from which the following three quotes are taken:

"Perhaps no single document offers us more insight into the workings of this fruitful dialectic between fact and fiction than Col. Crockett's Exploits and Adventures in Texas (1836), avowedly based on the hero's own diary, but in reality a clumsy fabrication assembled immediately after the fall of the Alamo out of less than the noblest of motives - pecuniary profit and political gain."

About the bee hunter:
"His counterpart in Col. Crockett's Exploits, however, reverses this sequence somewhat: a gentleman by birth, he bids farewell to his village fiancée and sets out for the Alamo with Crockett, only to prove the girl's fears that she will never see him again predictably prophetic. We hear the bee hunter even before we see him, as he sings a romantic song by the dawn's early light, and when we do get a glimpse of him, it is clear that he is less a trail-blazer than a dandy in buckskin, a dandy who, incidentally, enjoys the unqualified admiration of the author, Richard Penn Smith himself."

"In short, this bee hunter is a figure out of popular melodrama, transported incongruously to the wild west, and in comparison with which Cooper's Paul Hover is a model of rigorous verisimilitude. In this young worthy's propensity for spontaneous song, it is tempting to see a foreshadowing of Gene Autry and Roy Rogers"

It's possible the lines you are looking for are in the book. (A copy is available at High Ridge Books - Rare Books at $1200!).

Mick