Atmospheric pressure? Temperature? Electrical disturbances? The simple fact is, no one is quite sure how a storm bottle works. Or indeed how accurate it is.
Nevertheless aboard HMS Beagle during the Darwin Expeditions of 1831-36 Captain Robert Fitzroy developed and refined the storm bottle (invented in the mid 18th century) and suggested that changes in crystal formation could be used to predict quite subtle changes in the weather.
Now of course from a purely practical point of view there are sophisticated electronic weather stations that will give you a far more reliable local forecast.