In-Between the Beat
Harmonically, the weakest points of all fall in-between the beat. Your ear doesn't care as much what happens there. You can get away with a lot in-between the beat.
Getting comfortable playing various subdivisions of the beat will really open up possibilities in the basslines you create. Since you commonly have to play the "boring" notes on the beat, your most creative opportunities fall in-between the beats. Practice your rhythmic subdivisions!
Listen to Sting's bassline on the verses of So Lonely. The strong root notes of the chords all fall on the beat. (This is the classic I-V-vi-IV progression in C, by the way.) On a 16th note before the beat, he plays an approach note from a half-step below each root. These are weak scale and chromatic notes. They don't define the chord. Some are not even in the key. These "off" notes between the beat produce tension pulling you into the next root note.
The Police – So Lonely
In contrast, let's listen to one of my favorite rock riffs of all-time...
Cream - Politician
Jack Bruce, another great we've lost recently, breaks the “rule” here and puts the weak notes on the beat.
Notice how it has a harsher sound? Naturally, he did this on purpose. It sounds dirty and rotten...like a politician!
If you examine the rest of his bassline, it still outlines and defines the chords. The off-ness, however, comes from the placement of the weak notes on the beat. He's outlining the notes of a major triad adding a chromatic approach note before each chord tone: 7-R, b3-3, 7-R-7-R, b5-5, 7-R.
Jack Bruce understood the “rules” and knew how to creatively break them.
I hope this gives you some insight into why we, as bass players, can't blindly apply scales to our basslines. This is why I urge you to emphasize Chord Tones in your bass studies. As you learn to hear, find, and play these strong notes, you will learn to embellish them with scale and chromatic notes. It's really not that hard of a concept. You just need to be pointed in the right direction to put it all together.
I also want to reassure you that this whole process becomes intuitive. You don't sit down with staff paper and line up notes to beats. Instead, your hearing becomes organized. With practice, your musical mind internalizes this and takes over.
In upcoming lessons we'll apply these ideas in basslines, exercises, and suggested songs.