It looks like everybody and their brother recorded this little ditty.

The following is from a 1968 recording by Phil Harris.

THE PREACHER AND THE BEAR - As recorded by Phil Harris - Writer: Joe Arizona

[Bb] Now a preacher went out walkin'
Was [Eb] on one Sunday [Bb] morn'
It was against his religion
But he [C] took his gun a-[F] long
He [Bb] shot himself some mighty fine quail
And [Eb] one little "measly" [Bb] hare
But [Eb] on his way [Bb] returnin' home
He met a [F] great big grizzly [Bb] bear;

NARRATION: Well, the bear got down in the middle of the road
On all fours like a great big toad
And looked that preacher right square in the eye
And the preacher looked at him and said: "Bye-bye."
Started down the road and took out to run
The bear right after that preacher did come
Run and they run for about a mile
Then they both sat down and rested awhile
The preacher got up - started again
The bear he started out with more vim
They ran and they ran till he spotted a tree
Said: "Up on the limb is the place for me."
The bear got close - made a grab for him
Preacher leaps up and he made the limb
Pulled himself up and turns about
Cast his eyes to the skies and he did shout;

Refrain: "[Bb] Oh, Lawd, you delivered [Eb] Daniel from the lion's [Bb] den
Also delivered Jonah from the [C] belly of the whale and [F] then
The [Bb] Hebrew children from the fiery furnace
So the [Eb] good book do [Bb] declare
Yes! [Eb] Lord, if you can't [Bb] help me,
For goodness [F] sake don't help that [Bb] bear."

NARRATION: Just about then the limb let go
And the preacher came tumblin' down
Reached in his pocket, pulled his razor out
Just before he hit the ground
He hit the ground with an awful bang
It was a terrible sight
The preacher and the bear, with a razor in his hair
Just a-cuttin' left and right
Well, they rolled around on the ground
The preacher was up and then he was down
The bear let out an awful moan
It looked like the preacher was holdin' his own
"Lord, if I get out of here alive
That Good Book I will abide
I'll never sin on Sabbath day
And Sunday come, I'll pray and pray."
To the heavens, he did glance
Said; "Lord, just gimme one more chance."
Then his suspenders gave away
And he knocked that bear ten feet away
Then the preacher got up and made a bound
To the tree where he'd be safe and sound
Pulled himself up and turned about
Cast his eyes to the skies and he did shout:

Refrain:

Note. http://www.bmi.com lists several authors of similar renditions.