This from Phrase Finder:

: The cartoon voice I’m remembering sounded like Droopy. I think. Anyway, “Random House Historical Dictionary of American Slang, Volume 1, A-G” by J.E. Lighter, Random House, New York, 1994, has BUNKY, meaning “full of nonsense." 1918. It also has BUNKIE 1.a. Army & USMC, a bunkmate. 1858. b. student, a roommate. 1918. 2. Army, a friend, comrade. 1865. 3. used as a condescending term of direct address to a man. 1978, Superman 206: “Excuse me, bunkie. Don’t you have anything useful to do?

That makes sense. One of the websites I looked at after Bruce supplied the name and title said Eddie Lawrence developed the Old Philosopher routine while he was in the military. I was wondering whether bunky/bunkie was short for bunkmate.

The Old Philos. record (I guess the first one) reached #34 on the hit parade in 1956. Mr. Lawrence is now 80 years old.

"the Old Philosopher"
When did "the Old Philosopher" become "the Old Foolosopher"? Only at the Claridge? [Thanks for the up-date, Max.]

foolosopher

He would play with the term in his live shows, and hosts and MCs would introduce him as the Old Foolosopher...sometimes a critic or entertainment writer would use it in a review or story...but, officially, he was billed as The Old Philosopher.