This can be approached from a legal perspective or not. From a legal perspective based on the contract verbage it seems your tenant could be responsible. It would seem the reason for the high bill does not matter, whether it is a pipe burst or the tenant leaves a faucet running then go on vacation for a month. But I am not a lawyer. However, this then leads to what if your tenant disagree and does not pay? The water company will then cut off his/her service, and if left unpaid, depending on the jurisdiction, down here where I am they will then impose a lien on the property. regardless who's name is on the account.
For this reason I would suggest getting with the tenant and work something out where the burden can be split.
It's not your fault because you don't live there, can't be there to notice anything unusual, like noise behind the walls with water moving when no one is using water.
It's not your tenant's fault because they are not "in tune" with home maintenance. I have young tenants who does not know the difference between water supply pipes and drain pipes, totally clueless. They can take, edit, resize, annotate, add smilies and post a picture on a tiny phone with ease but can't change a light bulb or swap out a battery at the back of a wall clock, let alone keeping an eye on a buried pipe or a leaky water heater relief valve. They just expect things to work.
This is probably what I would do in your shoes.
First, I will contact the water department again. Many water bills have multiple components to the bill. In my town they charge me water usage and sewer usage. They assume the water being used is sent down the drain which they have to collect and treat, the sewer charge is actually more than the water charge. Of course this is not applicable when you are filling up a 25000 gallon swimming pool, so we could call them and say we are filling up a pool and have the sewer rate waived for the time the water is used for the fill. You should ask the water company to deduct out of the bill the sewer charge because they never made it to the drains for treatment, that should be on top of whatever consideration they gave you for the water leak.
You may also be able to work something out with the water company so the outstanding balance can be paid over a period of time.
It may be necessary for your tenant to call since the name on the account is not you. Perhaps a visit to the water company together for a scheduled appointment with a supervisor is best, but don't know if this is feasible with the coronvirus threat these days.
Whatever balance is outstanding after all these efforts I would probably propose to the tenant to split it after pointing out the clause in your lease.