You pay monthly, not quarterly, right? Extra 121,000 gallon of water in a quarter is also nothing to sneeze at, just changes the flow calculations a bit. I ask because many (most?) people pay for water quarterly.
Anyway, a back-of-the-envelope calculation turns up a flow of 2.8GPM - this is a flow of a nice (no low flow!) shower being on all the time the entire month - something you would absolutely feel and hear the hissing of the water flowing. Well, if it was in a quarter, it's still 0.9GPM flow - I'm not sure how could you miss that while visiting either although it would be much more gentle.
My thought was perhaps some good neighbors helped themselves to fill a pool using your outside spigot. But 121,000 gallons would make for a HUGE pool, 4-6 times what you might typically find in people's backyards, so I think your neighbors are good people, I feel embarrassed this thought crossed my mind :)
Is this a public sewer, BTW? I cannot imagine there's be no signs if this was a leak and you had a septic. How's your water heater hooked up? Any drains plumbed directly to sewer? Heater looks OK, water is hot?
I did have an instance once where my *quarterly* bill jumped 20,000 gallons one time but I chucked it up to irrigation - it was summer time, even though I would never knowingly use that much. I might have forgot to close a spigot (for a mighty long time). But now is winter time, assuming you are not from AU, so I imagine there would be no watering of plants this time.
This is an intriguing mystery, I'd love to know how's that possible myself. If you can add something to the info that's available, that would be nice. You can also post pictures here if necessary. Cheers!