…that don’t appear again in their songs.
If accompanied - like in the following (by guitar strums/licks every seven, I think) (and a basic drum beat) - as long as the bass is clearly the lead, then all good.
Video/audio not necessary.
May I mention Dear Prudence by The Beatles although the bass kicks in around the 18-second-mark. It has an understated but entirely pivotal bass. One of McCartney’s finest really.
Most people seem to be missing or ignoring the stipulation in the OP about the bass intro not repeating itself in the song - even those where the intro is different are mostly just a variation on the main bass riff. I wonder if there are any good examples of a bass intro completely different from the riff?
One of my personal favourites (which similarly does not conform with the OP) is Keep the Faith by Bon Jovi, a great bass intro and riff at the heart of the song.