No they won't. That isn't how insurance works. Transdev will make a claim against THEIR insurers, (assuming that they are not "self-insuring"). Their insurers insure the bus, and not the Range Rover driver's. Their insurers will decide whether the bus can be repaired or is beyond economic repair and they will then "write it off" if it is.
If they do that, then the bus will belong to them. They will pay Transdev the value of the bus and it is up to the insurer whether they crush the bus, or sell it for parts or sell it as a "damaged repairable". That is how the different categories of salvage operate. It depends which category it is placed in.
If Transdev want to buy it back for parts or as a "damaged repairable", then they can agree a price with the insurers if the insurers are willing to do that.
It will then be down to Transdev's insurers to recover their outlay from the Range Rover driver's insurers and establish that the accident was the fault of the Range Rover driver.
For those questioning whether Transdev have had the bus assessed already, the point is this - they are a large company, operating many buses, employing many qualified and experienced engineers who will have seen many damaged buses in their career and they will know whether a bus can be repaired or not and will have seen how badly the chassis is twisted etc. to know that it cannot be repaired.