It took me about 4 to 5 days to completely memorize the Bass fretboard using flashcards.
These in particular. I highly highly recommend it. Get your wife/girlfriend/friend to test you.
However, memorization and finger memory are two different things. So once you get the note-fret relationship down in your head, you have to spend additional time to get your fingers to know it, too. Then, you can navigate the bass by feel alone.