Martin, lest you are being confused, the button that plays the note E on the counterbass line is known as C counterbass.Therefore, yes, the pattern is as you descibe, with all three buttons in a line across the bass section.
BTW don't do as this fool did, and cripple your bass hand for years. You have five fingers on your left hand (I hope) Thumb No1, little finger No.5. Use No.4 for the counterbass and bass, No.3 for the major chords, and leave No.2 free for minors, major 7ths, and that outside row that only Sam plays.
Took me years to unlearn No.2 on the majors. PM me if you need any more, rather than getting Spaw all worked up about fish. At least that's safer than flatulence, Cletus!
Skipjack