The aforementioned bonus room has its own song, a lo-fi track accompanied by guitar with the lyrics written specifically for the level:
Here's a little bonus room, because I know you've had it tough.
Here's a little bonus tune, about collecting real cool stuff.
Yes, here's a little bonus room, where you can play.
Don't be frightened, don't run away.
The complete lyrics can be found in the related links section.
The game soundtrack by Terry S. Taylor, which features the infamous "bonus room" song with hilarious lyrics, is available on a double CD together with the soundtrack to "The Neverhood" and "BoomBots" (all three games ever released by The Neverhood, actually). It is called "Imaginarium" and is available through the website of Taylor's band Daniel Amos: http://danielamos.com/store/
There's something special to the game soundtrack here, apart from many levels featuring (mostly mumbled) lyrics in their music. Each level consists of several stages (three, in most cases). In the first stage of each level, you get a reduced version of the music, with the vocals and/or some instruments missing. Sometimes you just listen to the percussion first... The second, third or last stage of each level then features the whole set, so you have some kind of musical climax here. :-)
When you regularly start the game, you begin at the "Science Center". This is not the true first level, though. The real first level is called "Skullmonkey Gate" and is only accessible via level password. You see Klaymen falling from the sky in the intro screen to that level, so you get a quite neat transition from the FMV intro there. I don't know really why they decided to add it only as a bonus, but nothing much really happens there and the graphics and music aren't that impressive compared to the other levels. So I guess it was a decision based on the first impression the game ought to give.