Here is another one of my weird musical questions:

What wind instrument plays bass in the Password Plus theme? Bass saxophone?

Close but not quite. It's a baritone saxophone - the same instrument you can hear doubling the melody on the Lucky Numbers/High Rollers 1987 theme.

The bass saxophone does exist, but it's long since fallen out of common use. The most commonly used saxophones nowadays (in descending range) are alto, tenor, and baritone.

There's also a soprano sax, which is not curved like the rest of the saxophone family. You'd recognize it as the instrument that you wish Kenny G would be playing when he trips.

(EDIT: Upon further inspection of the not-great-quality copy I have, it sounds more like a bari sax doubled with a bass trombone)

Definitely bari sax, with the possibility of one of the low trombones (or a bass trombone) doubling on occasion. But you can definitely hear the reediness of the bari sax.