Could it be because the ballot is being run by a third party organization (Electoral Reform Services?) and it may take them a day or two to collate all the information before they release the results?
More likely I would say, is that the time is to give BASSA a chance for a last minute face saving deal with BA before they have to present the inevitable yes vote to the screaming mob at the race course.
If the court case goes their way, they will expect to use these couple of days to try and use that leverage to get a deal.
If the court case goes against them, they will try and use those days to get some sort of face saving measure.
Either way, they will be trying to avoid a strike if they have any common sense, because the troops simply don't have the metaphorical balls for it, and no matter how violently vocal a small minority (5-10%) get, your average part time mum cabin crew member at BA is going to bottle it and call in sick, or come running back, along with the commuters who will use the excuse of keeping their staff travel as a necessity.