Think of a bass as a big, simplified guitar, at least to start with. They're wonderful instruments and I've come to enjoy it as much as I enjoy playing the guitar.
So here's Synchro's guaranteed method of playing the bass in five minutes or less.
First: Start by playing whole notes of the root-note of every chord. It's the simplest bass line in the world and it's completely correct, albeit a bit boring and predictable.
Second: Add an alternating bass line by alternating between the root and the fifth. For a C chord alternate between C & G, for an F chord F & C and for a G7 alternate between G & D. Something interesting happens, you get some simple lead-in notes for freebies. When you play the alternate of the G7 the D note leads you back to the root of the C chord.
Third: Learn to play some simple walk-ups and walk-downs. We're talking simple here, think of the bass line from a Polka. All you need to do is play the notes out of the scale that go between the roots of the chords you're changing between. As an example from G7 to C you can play G, G, A, B which leads you to the root note of the C.
Fourth: Spend some serious time with the Blues. You can start with a very simple (and somewhat trite) bass line based upon a Major pentatonic. For the C chord play C, E, G, A, C (one octave up), A, G, E and then for the F chord play F, A, C, D, F (one octave up), D, C, A and for the G chord play G, B, D, E, F, E, D, B. Beyond that you can start to experiment with passing tones and all sorts of other variations. There's plenty of examples to copy in the Blues, very fertile ground.
Fifth: Explore the minor keys. In minor keys flatted fifths are more common. There are a few pitfalls and some different changes (like the bVI - V change from "The Thrill is Gone".
Sixth: Once you know your way around both Major and minor keys even the most complex changes will be accessible to you and you'll become very popular at jam sessions.
