This article is from the Rec.music.makers.bass FAQ, by Kalle Kivimaa Kalle.Kivimaa@hut.fi with numerous contributions by others.
Standard music notation is written for bass in exactly the same
way that it is for piano, except that it is written one octave
higher than played; that is, the note to be played on the bass is
one octave lower than the one written on the page. This is done to
avoid using a very large number of ledger lines, since most bass
parts go well below the lowest line of the bass clef.
For example, the lowest note on a 4-string bass, open E, would be written
-------|------------------- (lowest line of staff) | ---O---