For my bass guitar I like to look at the tone knob as a "hot" or "cold" type situation.
Hot: This is when you want to cut through, or you have a prominent part. In the case of the bass, if I have a finger-style solo the tone knob is up pretty high. If I have a moving part in mid-range, it's up about half way. Cranking the tone up tends to sound more gain-y, so your finger noise tends to become more pronounced, so I never crank it up all the way, If I'm slapping this is up fairly high but dialed back a bit. I want to favor the bridge pickup and I want my slaps to bite but not be overly-loud or boomy.
Cold: This is when you want to mix. Dial down the tone knob too much and you might get lost in the mix. For a bassist, this isn't so bad. As a bass player you typically provide the foundation. If I want to be felt, but not heard, I'll dial my tone down. This can also affect volume, so you have to compensate. If I'm laying down a funky fingerstyle groove I'll dial it up a bit, since the bass line will likely drive a lot of movement, but never more than half. We don't want to step on the toes of the melodic players.