Purchase or download a bass guitar note chart. A note chart will show you what note every finger position on the fretboard is, and it can be used for reference when you are practicing your instrument as well as without. Note charts often come in beginning bass guitar instruction books, which may be useful for new players. If you don't want to purchase a book, many different websites have them available to look at or download for free.
Put colored gum-free stickers on each position on the fretboard. Label the stickers with a waterproof marker using the chord chart. Having the individual positions labeled on the fretboard will help you to memorize the notes while playing as you look at your bass. For the best results, use this in conjunction with a note chart while practicing.
Learn the most commonly played bass scales. The most common five scales that are used in a variety of different styles of music are the major scale, minor scale, pentatonic scale, minor pentatonic scale and blues scale. Knowing these basic scales in a few different positions will help you greatly in understanding the way the note layout of the bass guitar, and it will also help you memorize the note patterns that are common in different styles of music. When learning guitar scales, you can either purchase a book or find the scales on-line, though many players find that a book is more convenient and a bit easier to follow.
Learn to read guitar tablature and translate the tablature into notes. While this may sound like a boring task, it will teach you to relate finger positions to note names. After translating the guitar tab to notes, try to play the music by just looking at the notes. This may be difficult at first, but it will help to cement your knowledge of the different places where notes fall.