IF the monitors are sufficient to do a good job of monitoring instruments (meaning that they're bi-amped AND there's a separate mix for each musician/vocalist) then my amp becomes my personal monitor and I don't need to worry about whether anyone else can hear my amp- that's what the monitors are for.
But, I've only been in that situation three times. Mostly they say they have monitors for isntruments, but they're really only suited for vocals. In that case, putting any electric instrument into the monitors is going to make the vocals harder to hear, and that's going to exacerbate the volume wars. So, if it's vocal-only monitors, but the FOH is good and sufficient to the gig, then my bass amp is the monitor for the whole band. Set up in a fashion that lets every one hear me as well as they need. A big monitor on the high-hat side would have to be freakin' HUGE to effectively block the bass amp's sound enough to be an issue. I used to use a pair of Euphonic-Audio VL-208s with my Eden WT-400 for gigs like that. I'd set it up behind the PA stack on the snare-side of stage (I stood right next to the drummer with no one on my right). I angled it back towards the drummer so he and I could hear great, and it was enough wash for everyone else. And it totally removed my amp from conflicting with FOH.
jte