OK, if you know the major modes, the thing we need to think about here is the relationship between key and chords.
The modes are just a way of arranging the 7 notes in any key into one octave sequences on the fingerboard for ease of access (OK, they take on a bigger significance if we start writing 'modal' compositions, but for now, we'll stick with things in one key at a time!)
So as bassists, what we get are the seven notes in the key arranged in a fashion where we have a pattern with each possible root note at the bottom of its own mode.
The next level of breakdown we need to get under our fingers (actually, it's the first level of breakdown we need to get under our fingers, but as you know the modes already, we'll think of this as the second for now...) are the seven arpeggios in each key - root, third, fifth and seventh. If you take each of the modes as you play then, and instead of just playing from the bottom to the top, play only the 1st, 3rd, 5th and 7th notes. These are the 7th chord arpeggios that relate to a key. These are the notes that are specific to each chord.
However, they aren't the only ones that will work. all the other notes in a particular key will work over the chords, they'll just imply different levels of tension and resolution (which after is what harmony is all about - resolution moving to tension and back again...)
So we've got some kind of harmonic hierarchy now - we have chord notes and we have, for want of a better word 'colour' tones - the 2nd, 4th and 6th notes of each mode.
What this means is that ultimately, any note in the key can work over any chord in the key. The artistic decision is to decide which ones are the 'good notes'. The notes in the chord are going to be neccesary for outlining the movement of the chords. The 'colour' notes are going to increase the ambiguity of the progression if you use a lot of them in the bassline, and are going to help to make your playing sound more melodic and less like a slightly stilted walking jazz line.
So what to practice? Get those 7 arpeggios down, so that you can play them in any key (BTW, 'play in any key' doesn't mean that you have to practice them religiously in all 12 keys, it just means that you have to know them as they relate to one another as a pattern, rather than only knowing them relating to a fixed root. So if you can play all 7 in C, A and Eb, and can switch from one to the other, chances are you're doing OK... nothing wrong with pracising them in all keys, just not totally neccesary...)
Now, as soon as you can, get yourself some sort of chordal accompaniment to play over - could be band in a box, could you you recording some chords onto a tape deck, could be an Abersold play along, best of all, get a looper of some kind, and start to make some music. Start to make some musical decisions about the sounds you like and the ones you don't like. The notes that work for you and the ones that don't. The kind of lines that sound jazzy and the ones that sound like funk.
The arpeggios and modes are just mathmatical and geometric relationships. The music is in how you play them, how you relate those shapes to what you hear. Start with just a one chord vamp if you like, but make some music. Don't get bogged down in just doing exercises. All those exercises can be made into music by contextualising them. It's not hard, and it makes practicing a whole lot more fun...
cheers
Steve
www.stevelawson.net