Nothing to stop you buying the text books, downloading the syllabus and cracking on.
You would have to pay to take the exams at a private candidates centre yourself (unless your school agreed to enter you for it, they are an exam centre so it does not really matter that they do not offer it).
Back in my 6th form days i can imagine the teachers would have said doing this was nigh on impossible.
However with online resources, including assess to practice questions, mark schemes ectera its far easier nowadays, if you are driven enough to do it i believe its achievable.
I did A level Ancient History entirely on my own, to let you know something of the workload i spent c500 hours on it (over 16 months) and received a grade A.
One more thing, the school may feel a bit put out at your sparse timetable with only 2 A levels and using their premises and resources to study a third externally (though any educationalist worth his salt in my opinion should not be bothered).
So maybe choose a third subject at AS?
You could always drop it later, and pay it lip service in the meantime (cynical i know).