OP - The concierge at the IC will know both the courier company and the few drivers who have that route. He may well have mobile numbers and may be able to track down your bag with the courier company.
Even if he doesn't BA ought to be able to supply you with the company's name. Armed with that number, a call by you may get the bag to the IC.
While it is BA's responsibility to get the bag to your hotel, once it is with the courier, the best air carrier is stuck with the industry or sloth of the courier.