Abosolute best case, as theve already admitted liabilliaty by leaving thier details, you can demand that the full Cost of Repaires to your satisfaction are are paid and covered by them, this can be done in two ways -
1. You submit a Quotation for the Cost of Repairs and they front the Cost in Full prior to the Works if paying you directly, or they agree to to pay the Repairers directly using an agreeable method between them and the Repair Co. either way you will need to get something in writing that leaves a paper trial so that you still have a legal claim of sorts should it not go to plan. If the Bus is run by outside Contractor, which is probably the case, then then Bus Contractors may suggest they cover the Cost by using there Own or there Approved Repairers directly, but your still need written confirmation prior to the event.
2. They dont want to play ball on any of the above, then you inform them you will be going down the Independent Insurance Assessor route, the Insurance Assessor will work on your behalf without involving your Insurance, He will (or Should) claim his full costs and yours against their Insurance Co, and your probably find he will also claim additions, like, Hire Car or Travel Cost, Loss of Earnings etc, whilst the Car is undergoing repairs.