The Hal Leonard books teach the 124 method. Bass Method by Hal Leonard.
Personally, i have an issue with it, as it seems like a habit that becomes hard to break. In a way, i wish i could "unlearn" the 124 method, as i seem to use it too much on the upper frets.
If what you play sound good, then you have no need to change.
But if you are looking for an idea to practice and develop into your playing then try developing chromatic scales.
If we look at the way a standard bass is set up and tuned we always have options for the same note one fret to the left or right on a new string when playing 1234.
I call working out fingering options as " fret mapping", this is just a way of examining what fingerings are possible to use and what ones are best to use. The chromatic exercise i mentioned will open up the ideas of this and help see and hear more options.
For example "A" chromatic scale over two octaves what are the options?
The key ( nothing to do with music it is the key to the terms used) is the open string and the fret number being used, this has nothing to do with intervals or chord tone numberings, this is purely fret numbers.
So the open strings are named as such, E-A-D-G then the fret number is named to that string
A5= D,
D6= G#,
E= E,
E1= F,
E3 = G,etc
So one option to play "A" chromatic over two octaves are ex1.
A chromatically to A20 (A-A20)
D16 chromatically to D19 (D16-D19)
or another option is ex.2
E5-E20
A16-A19
D15-D18
G14
or another option ex.3
E5-E12
A8-A15
D11-D18
G14
or another option ex4
E5-E8
A4-A7
D3-D6
G2-G14
So now you have the idea of fret mapping, this is just a few of the options for A over two octaves. All we do is learn the options we have rather the any pattern. Once the best option has been choosen, then look for a pattern to learn if need be.
But any fretting postions need to maximize fingerings to make a complete fret map.
As a rule we want to optimize the use of all 4 fingers on the fretting hand following on from each other, so if i call the fingering key, 0-1-2-3-4 then
0 when used is an open string,
1= forefinger,
2= middlefinger,
3= ringfinger,
4= littlefinger
Using "A" chromatic over two octaves again ( because it is familier to us as an example) then what fingering options do we have?
Remember each number represents a finger.
Once we get familier with it we learn to associate the fingers used with the fretting used.
I will touch on why this is so at the end because it is an associated learning that happens....something you become aware of.
Because the fretting is always a new note to the left or right then any repeat numbering is a new note for the numbered finger, again remember each note is fretted once.
Its fair to say our mapping will not follow an even fingering of fours, so the option is to use open strings, move the fingering at the start or at the end. so a fingering may start
0-1-2-3-4-1-2-3-4 etc
1-2-1-2-3-4-1-2-3-4 etc
or end 1-2-3-4-1-2-3-4-1.
So looking again at ex.1
A chromatically to A20 (A-A20) the fingering is 0-1-2-3-4-1-2-3-4-1-2-3-4-1-2-3-4-1-2-3-4
D16 chromatically to D19 (D16-D19) becomes 1-2-3-4
ex.2
E5-E20 =1-2-3-4-1-2-3-4-1-2-3-4-1-2-3-4
A16-A19 = 1-2-3-4
D15-D18= 1-2-3-4
G14=1
ex.3
E5-E12 = 1-2-3-4-1-2-3-4
A8-A15 = 1-2-3-4-1-2-3-4
D11-D18 = 1-2-3-4
G14= 1
ex.4
E5-E8 = 1-2-3-4
A4-A7 = 1-2-3-4
D3-D6 = 1-2-3-4
G2-G14 = 1-2-3-4-1-2-3-4-1-2-3-4-1
In ex.4 G2-G14 is one option, another may be
1-1-2-3-4-1-2-3-4-1-2-3-4 or
1-2-3-4-1-2-3-4-1-2-3-4-4
I said earlier about an associated learning with the fingering.
If you have been working on these exercises you will associate that
A -A12
means the hand had to move three times so the the little finger landed on A12 ( the octave) 3x4 = 12.
As we use it we start to associate notes, fret positions, fingerings as one.
Once we start to see and hear A7-8-9-10
as E-F-F#-G then the mapping is becoming internalized and part of the playing skills we draw on.
This means when we see Standard Notation and read the notes
of say a simple latin triad line of
A-C#-D-C#/D-F#-A-F#/E-G#-B-G#/D-F#-A -F#/A-C#-D-C#
We can follow paterns or notes or a combination of them.
This is because in music we are always coming to, staying on passing through, and leaving chord changes and any associated harmony involved. so fretting options for these triads can be
E5-A4-A7-A4/A5-D4-D7-D4/A7-D6-D9-D6/A5-D4-D7-D4/E5-A4-A7-A4
or
E5-A4-D2-A4/A5-D4-G2-D4/A7-D6-G4-D6/A5-D4-G2-D4/E5-A4-D2-A4
or combinations of those two such as
E5-A4-A7-A4/A5-D4-D7-D4/A7-D6-G4-D6/A5-D4-D7-D4/E5-A4-A7-A4
or
E5-A4-D2-A4/A5-D4-G2-D4/A7-D6-G4-D6/A5-D4-D7-D4/E5-A4-D2-A4
These are just some of the options, more include the use of open strings, a new D2-G1-G4 to replace any of the E triads etc.
Fret mapping is just about exploring and learning what notes are available to use to fit any playing situation. Its as a skill that once learned never really needs any more thought.
When we read we associate the notes to the fret position, and when ever fret numbers are used we associate the notes to them as a matter of course rather than any pre-planned labouries process