Well, for starters each fret on the bass is a half step on the piano. So, here are the notes for your bass guitar:
4-string
Starting with the 4th string (thinnest) = G (open), G#/Ab (1st fret), A (2nd fret), A#/Bb (3rd fret), B/Cb (4th fret), B#/C (5th), etc.
Starting with the 3rd string = D (open), D#/Eb (1st fret), E/Fb (2nd fret), E#/F (3rd fret), F#/Gb (4th fret), G (5th), etc.
Starting with the 2nd string = A (open), A#/Bb (1st fret), B/Cb (2nd fret), B#/C (3rd fret), C#/Db (4th fret), D (5th), etc.
Starting with the 1st string (thickest) = E/Fb (open), E#/F (1st fret), F#/Gb (2nd fret), G (3rd fret), G#/Ab (4th fret), A (5th), etc.
5-string *Same as the 4th string, except there is an even thicker string added
Starting with the 5th string (thinnest) = G (open), G#/Ab (1st fret), A (2nd fret), A#/Bb (3rd fret), B/Cb (4th fret), B#/C (5th), etc.
Starting with the 4th string = D (open), D#/Eb (1st fret), E/Fb (2nd fret), E#/F (3rd fret), F#/Gb (4th fret), G (5th), etc.
Starting with the 3rd string = A (open), A#/Bb (1st fret), B/Cb (2nd fret), B#/C (3rd fret), C#/Db (4th fret), D (5th), etc.
Starting with the 2nd string = E/Fb (open), E#/F (1st fret), F#/Gb (2nd fret), G (3rd fret), G#/Ab (4th fret), A (5th), etc.
Starting with the 1st string (thickest) = B/Cb (open), B#/C (1st fret), C#/Db (2nd fret), D (3rd fret), D#/Eb (4th fret), E/Fb (5th), etc.
*And the cycle continues as you add on strings.
Notice that as you go from the 1st string to the 4th string (right to left), the notes move in 5ths. So, studying the circle of 5ths will help you to learn notes as you move that way. (G, D, A, E, B)
Also, notice that as you go from the 4th string to the 1st string (left to right), the notes move in 4ths. So, studying the circle of 4ths will help you to learn notes as you move that way. (B, E, A, D, G)
I hope this helps you out!!!