Taken from BA (which is why I decided to fly with Virgin last year as it is completely free!)….
There is no additional allowance for sporting equipment (inc. bicycles), but it can be carried free of charge as part of your free checked baggage allowance.
If the total number of bags is more than your free checked allowance, you will need to pay extra bag charges.
So take you main bag under 23kg which is free – then add one additional bag (for the bike) and keep it under 23kgs which will be charged depending on the type of ticket you have, i.e. Euro Traveller UK Domestic = £30, Club Europe (2nd bag is free) or World Travller = £34.
But to get these prices you need to do it online through your ‘Manage Your Booking’ on BA.com – otherwise the charges are higher if you pay at the airport (i.e. £35, £35 or £40).