There are many different ways to approach playing bass and depending on what style you are trying to go for it may be all you need to fill the sound. I'll explain a few simple styles and techniques that can spice up a bass line.
Rather simple, but effective. Your still playing only the root note, but changing the octave is a very simple and effective way to make the bass line pop a little more as the octave jump will stand out and is used a lot when creating bass lines.
A little more movement you can move from the root note of a chord to the other notes of the chord. For example if you start out playing the root note of a G major chord you can play the 3rd (B) or 5th (D) of the chord no problem. As long as you start on the root and play chord tones you should be fine. Even simpler most bassist when they arpeggiate only uses the root, fifth, and octave above. It's simple but it's effective and is used in many different techniques including alberti bass (for piano).
A very effective method utilize non-chord tones as a bassist is to move step wise to move from one chord to another. For example if the harmony was going from a C to Dm, you could play the root note C and then play a C# before you play the root of the Dm chord. Again very simple, but effective. Another example is if you were going from Dm to F, you could play an E while transitioning between the two chords as mentioned above.
Pretty much a combination of everything mentioned above. It's a very nice technique to learn as a bassist even if you don't play songs that would work with this technique because you learn how to "move" a lot as a bassist. Here is more detail on how to create a walking bass line.
There are other techniques, but try to explore these first. At the end of the day do what sounds good to you.