I'm having trouble trying to find a particular version of the song

Last year Quartet Records released the soundtrack with most of the versions heard in the film;

http://www.quartetrecords.com/composers/john-williams/the-long-goodbye.html


Unfortunately the CD sold out quite fast, but you can probably find a copy on Ebay or from one of the various sites selling soundtracks. (I think it's going for crazy prices though)

I have the CD, & I think the specific version of The Long Goodbye you are referring to is only found within a 10 minute medley on the CD - most of the versions you hear in the beginning of the film are in the medley, & are no longer than what you hear in the film. Either the master tapes of the complete renditions were lost, or only brief snippets of each version were recorded to fit within the intro titles of the film, as Marlowe drives to the supermarket to get the cat food. I don't know, but reading the notes on Quartet's website, it seems that the weren't able to find all of the tapes containing all of the music recorded for the film. (The CD is still worth getting though - it's a great soundtrack)

It's a shame, because I was looking forward to hearing that same version of the song that you are enquiring about, only to find that it's roughly 8 seconds long on the CD, same as the bit you hear in the film.