Been recently enlightened on overdrive. Curious how other players use it.
School me on how you use it!
I don't feel like any of the options really explain my position, so carrots.
It depends largely on musical context, but if the music allows for it, I will tend to choose to use drive or some other dirt. In my rock and blues covers/originals band, the drives come on and off, but in my other band which is entirely original and heavier grunge rock, it's more often than not for my tone to be driven to some degree.
The overdrive is on for many songs, but sometimes what I do is make use of a compressor either before or after the drive to allow me to turn my bass volume down and clean up the drive. The compressor just softens the dynamic impact of turning down, because otherwise if I turn down the signal becomes too quiet to hear without bumping a master volume up somewhere. I can turn down about a third on the volume and still be audible but not have any drive on the sound.
Sometimes with this arrangement I will play with the "clean" sound for quieter parts and then turn up for loud parts, much like guitarists would. Occasionally I like playing with the overdrive on in this "clean" configuration because it's just a nice, warm sound.
For pedals, I use the Broughton Audio Azure Drive, which is a clone of the Blueberry Bass Overdrive. It's very mid-forward, sounds a lot like amp distortion. I also use the Broughton Locust Star, which is a clone of the RAT distortion. It can get very gnarly as it is a distortion, but the LS's case is a little special in that A) it runs at double the incoming voltage up to something like 33V, so if you give it 9 it runs at 18. This affords it the dynamic range to work as an overdrive. B) it has the option to use LED clipping, which to my ear can sometimes work a little better for overdrive sounds (think grindy amp distortion). The EQ is also powerful when it comes to getting your tone to sit the way you want it to in the mix.
The rest of my dirt pedals mostly fall into "fuzz", which I feel probably is outside of the scope of this discussion.