I heard just recently that a semi-famous jazz musician wrote much of the music that’s used for cartoons. Is this true? What was his name and is there a CD out of his songs?
Depends on your definition of “semi-famous”, “jazz”, and “cartoons” 
You might be thinking of Raymond Scott & Warner Bros. A lot of Looney Tunes (with music arranged by Carl Stalling) used a bunch of Raymond Scott’s melodies – most notably, “Powerhouse” (if you hear it, you’ll recognize it. It’s the one that goes doodlydoodly doodlydooodly bump ba bump ba bum…) There’s a Carl Stalling CD (“The Carl Stalling Project”) full of musical cues from WB cartoons, and a Raymond Scott CD (“Reckless Nights and Turkish Twilights”) both available at amazon.com.
And both right in front of me here at work. There was supposed to be a second volume of “The Carl Stalling Project” but I haven’t seen it.
There are several tunes on “Reckless Nights and Turkish Twilights” that will be familiar. Powerhouse #1 and #2, The Toy Trumpet, and Dinner Music for a Pack of Hungry Cannibals being the most likely to evoke images of Bugs and Daffy.
The Raymond Scott CD is on Columbia, the Carl Stalling Project is on Warner Bros.
It’s available, I picked up a copy a few years ago.
As for Raymond Scott, I can’t hear “In An 18th Century Drawing Room” without imaging Granny coming into the room to check on Tweety. Amazon has listings for a couple other Scott CDs that sound absolutely fascinating.
The reference to a jazz musician doing music for cartoons may also be Vince Guaraldi, who wrote music for the Peanuts TV specials. Just picture one of those shows in your mind and you’ll hear a trio of piano, bass and drums. It was considered a rather daring choice at the time, but it turned out beautifully.
Quite a few of the songs from Bugs Bunny cartoons were written by the great Harry Warren. Warren was one of the top composers of his day and happened to be a staff composer for Warner Brothers, so they could use his melodies without paying royalties. The best collection of his work was Lullabye of Broadway: The Best of Busy Berkeley at Warner Brothers. Note Warren’s name isn’t part of the title – he was consistently overlooked (when they did a musical on Broadway of his tunes, his name was also deeply buried, despite the fact that everyone knows his tunes).