Hrm, ...I don't think, if you're carrying a monopod anyway, that having it hanging as far off your center of gravity as possible by using bag straps is necesarily the way.
When I was younger I had an improvised belt-clip that'd let me carry things to the shoot, and the monopod would usually be either on a camera or cached away somewhere for the duration.
I did used to carry a Maglite for nocturnal scavenging expeditions, and found it actually most comfortable to hang it from one of those plastic loops I mentioned before (not like the clips someone showed) usually right from the small of the back... that was the least uncomfortable to walk with, and it was accessible to me from either side. (Now you can get these little 'Dana Scully' jobbies with the little lithium batteries. I usually carry one of those, now cause I seem to have a habit of using round black objects in dim places.
)
Probably a matter of trial and error to find what's comfortable. The little setup I'm (not actually really much, yet, at least,) using now is mostly just to keep my hands free so I can get the monopod *to* a place I might want to use it. I've carried a shoulder bag of one kind or another on the same shoulder for an awful lot of my life, so, wouldn't be surprised if my back took a set, anyway.