As with my first lesson, my excercise is a hybrid of what I've found on the internet, as well as of my own invention.
Realizing to become a better player, not to mention an "accomplished" player, I needed to learn all the notes on my instrument, top to bottom. With a 20 fret/4 string bass, that can be a lot of notes!
One excercise I adapted is a hybrid of the "Note Finder." I begin with the open "E", and locate all the other "E's" on all strings. I then move to "F," and continue through "D."
As you play each note, I think it helps if you say aloud the note. Also, repeat the process back down the neck to the starting note.
The original excercise also called for finding all chromatic notes. You can, of course, do this, too. However, I felt if I learned where all the natural notes are, surely I could find a #'d or b'd note.; )
Another excercise I came up with involves using the moveable major scale pattern. If you aren't familiar with it, here it is:
This is the "C Major" scale, and where I begin. This is the only major scale with all natural notes (i.e., no sharps/flats). Play the scale up and down, and say aloud each note.
From there, I play the "D Major" scale, and say the notes, up and down.
(To play the D major scale, simply slide the pattern up the neck (2 frets) and begin on the "D" (3rd string, 5th fret. Hence the name, "moveable pattern.")
I play up to the "F Major" scale (starting on the 3rd string), and then drop the pattern to the 4th string for "G" through "C."
I don't spend a ton of time on these, but I do use them a combination warm-up/learning tool.
If you're familiar with the various scale modes, for variation, you can do the same excercise with different modes.
If you aren't familiar with modes, congratulate yourself because by learning the above pattern, you just learned one of the seven...the Ionian Mode!
The thing I like about these excercises, as opposed to simply playing chromatically up the string, is that you not only learn the notes, but you learn where they are relative to each other.
Hope this helps!