As a bassist myself, who gets "bored" quickly by this routine, and likes the bass to be just as much of an instrument as a keyboard, saxophone, guitar, etc. then I have needed to know how I can push past this, without the bass being an overpowering instrument.

The best ways I have found to do this, is to do this away from a band practise where I can focus my time on my instrument and use a program such as Guitar Pro, or Logic to outline the basics of the chord patterns and how they work.  Using these, I can also listen to the chords play over and over and figure out the best bassline for me - one that is not overpowering, can be somewhat complex, within my own capabilities to play, and most importantly fits in with the tone of the song.

As I am a very nice person, I have some examples to show of how you can move a basic chord progression and by very simply advancing through it to make an interesting bassline in this sort of style which hopefully you can take my way of working it out and move forward through it yourself.

I have started with a very simple chord progression, where the root note is hit at the change of each chord.

The next step is to hit these same root notes on every beat.

The final example places a "linking" note just before the change of each chord.  For this, I have used a note that is in the scale, not used at all within the riff, and is easily reachable to go between.  It also resembles a "common denomitor" and ends up giving a sense of structure, at least in the early stages.

As you can now tell, this bassline is very simple, and much more fun to play!  It is also very fitting for the slower songs and gives the band a memorable beat and timing point which can be extremely handy in the initial songwriting process.  I have used this bassline before, and the drummer even told me that it was how he remembers the tempo of the song!