Expanding

Well, it is a chord notation, so you could play other chord members. In this case the basic chord is C, E, G and then you could, depending on the style of the music, play the extentions. In this case Bb, D. There are 'color' notes and in this case A or B would work. Looking at altered chord tone (and there are quite a few) could spice things up also. And then after that consider passing tones. They could be any number of different notes depending on how you end the measure and what chord is coming up next.
Or the other answer would be... play whatever you think sounds good, and wait for people to bitch.

 

You can shake things up easily by leaving out a bass note on beat one - called a "one drop." It's easy to overdo it, but I love the way it feels and sounds. Or listen to Jaco's bass lines for examples of starting a bass line on notes other than the root. In particular check out "Havona" by Weather Report and their live version of "Teen Town" from the album 8:30. James Jamerson is another good player to learn from, his lines are interesting and provide a great groove and are more than just root notes. Listen to some of Chuck Rainey's work as well. He played bass on the Sanford and Son theme which has a cool bass line, but he's also done TONS of other stuff.

Then after you've learned how to do all that, go back to playing real bass. There's a reason bass players play that way.

 

Malcolm Amos should be alone shortly to add his chart but basically step one for me was to start root, 5. From there it was adding triads and as I learned the other chord tones I dropped the third in most instances. Then it was approaching the next chord with a chromatic walk From there it was sliding up and down to the tone I wanted from a half step away......

But that is just the note choice, the real first step along with R, 5 for me was in syncopation and getting away from just providing a straight 1/8th note pulse of the written root

 

A first inversion is a good trick, and gives the harmony a whole different feel. For instance, playing the third (in this case E) is great for when the chord is moving from I to IV. Or, another good one when the chords are going from I to V is to go ahead and play the V (G) while still on the I chord (second inversion), in anticipation of the V chord.