I recall when I first started playing bass, these articles were right on the front page
http://www.talkbass.com/forum/forumdisplay.php?f=90
Now they're slightly less out in the open, but they still have a lot of valuable knowledge if you haven't read it yet. The two articles at the bottom "Introduction to Scale and Chord Theory" along with "Bassline Construction" were especially helpful for me as I was starting out.
Anyways, looking at what you posted with Cliff's bassline, I'd say to learn to get familiar with the different chord shapes/patterns along the neck of the bass. Just taking a quick glance at it I noticed that if Cliff was playing along with an open E, then he was using fairly standard notes to play along. The 7th fret is always (unless you're playing in a non-standard tuning) going to be a fifth of the string it's on, and an octave of the string below it (well...physically, the string above it). While the 5th fret is always going to be a fourth of the string it's being played on.
So just taking a quick peek at the line you posted, I know he's using mostly roots, fourths, fifths, and octaves. In the case of the key they're playing in (E minor E, F#, G, A, B, C, D, E (octave)) the root, fourth and fifth would be E, A, and B as they're the first (root), fourth, and fifth notes in that scale. Using roots, fourths, and fifths are common in most basslines as they're probably the most pleasing to the ear. The only note that doesn't belong in that key is the 6th fret on the E string, or A#, although that's no problem really. You'll learn after playing a few songs that a lot of bassists tend to go outside of the scale when making bass lines, which is perfectly fine. Scales and chords aren't a rigid system of rules that you have to follow, but just a set of guidelines to get you started.