To play the major scale on the bass guitar. Use diagram below as an illustration:

The formula for major scale is

                                          T  T  ST  T  T  T  ST

T    =   Tone
ST  =   Semi tone

So if we take our root from C

We have:

C  D  E  F  G  A  B and back to C
d   r   m  f   s   l    t   and back to d

Major scale on the bass guitar

Now we started on the fourth string. The white dot serves as the root noted which is C(doh). We started on the fourth to the third to the second. 

the numbers on the black and white dots stand for the fingers you would use:

4   pinky finger(smallest finger)
3   ring finger
2   middle finger
1   pointer finger

The thumb(the fat finger stays behind the fret board)

So starting from the fourth string: 2 4 
To the third string                          1 2 4 
To the second string                       1 3 4

Look at the video illustration below for a clearer approach


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