Hi I am not pro, but can help you out alittle.
For western pop music, the chromatic scale has twelve tones. So all are valid.
If you meant the diatonic scale, there are 7. That would be tonic (aka root or 1), supertonic (aka 2), mediant (aka 3), subdominant (aka 4), dominant (aka 5), submediant (aka 6), leading (aka 7).
To understand what notes are sharp/flat for a scale, do use the circle of fifth chart.
http://en.wikipedia.org/wiki/Circle_of_fifths
A Major has 3 sharps, they are at F#, C# and G#.
So in key of A Major, the diatonic are A, B, C#, D, E, F#, G#.
Hoped you've been practicing your scales. In fact, if you memorized the semitones relationship from the root, you dont even need to memorize where are the sharped/flatted notes. For example, 2 is 2 semitone away from 1, 4 is 1 semitone away from 3 etc. It makes sense memorizing semitone relationship on fretted instrument like a bass guitar because the 'shape' of the fingering remains.
What notes to play (or not to play) will depend on the chords for the song. For bassist, I think what is important is to recognise and memorize chord formula.
Am listing down the more common chords:
Major = 1-3-5
Minor = 1-b3-5
Major7 = 1-3-5-7
Minor7 = 1-b3-5-b7
Seventh = 1-3-5-b7
Diminished = 1-b3-b5
Diminished7= 1-b3-b5-bb7
Augmented = 1-3-#5
Hope you noticed in the formula, some of the notes arent diatonic (eg Minor chord has flatted 3).
If what you're looking for are the notes for walking bass lines, it would be a different topic as you have to decide on tonic or chromatic notes, based on your current note and the target note, and also the duration between them.
If you want to learn music theory, you should grab the Rudiments of Music book.
http://en.wikipedia.org/wiki/Rudiments_of_music
All music (book) shop should carry it.