It's not clear to me that you really know what you're asking, without challenging your assumptions a little. Either that, or I'm completely misunderstanding the question.
It seems to me that fills and runs are inherently
flashy, to one extent or another. Although you can always play them with a more subdued tone, and/or with a less aggressive attack, the best way to make them more subtle is simply to play fewer notes
I have no idea idea of the genre(s) of music you play, nor of how much of your musical space legitimately
"needs to be filled". But I will say that, with the bass most particularly, "less is often more". A skilled player will often know how to say far more with the rests than he could ever say with the notes.
If you've never done so before, I would suggest that you take some time to ponder and meditate on that concept for awhile. Then come back to your musical dilemma - and find out whether you still see it the same way as you did before.