@Tyler Warner I'll start with a potential source of the leak - from personal experience. Toilet flapper. My rental hit me with a $300 water/sewer bill during a month that it was unoccupied. Turns out the seller used the toilet on the last day and the flapper stuck open resulting in 23,000 gallons of water going down the drain. It's sneaky because you can't always hear them, especially if the bathroom door is closed after use.
As for how to handle the tenant, I would not get yourself added to the utility, unless you can do so without admitting financial liability. Rather, I'd be proactively involved with the tenant and a plumber to try to ID the problem. If the house had an outdoor spigot and that spigot leaked after the tenant occupied, and it was not leaking before occupancy- technically it is your problem to fix the leak, but not your responsibility for the water bill. That would be on the tenant to ensure the spigot was off after they last used it.
But as you said, if your tenants are excellent tenants, I would do all I could within reason to help them resolve this. It is up to you to decide what is 'within reason'.