Białystok is the largest city in north-eastern Poland and the capital of Podlachia voivodeship. Public transportation between Białystok and Warszawa (the capital of Poland) is very convenient and provided by buses and trains.
The closest Polish public international airport is the Warsaw Chopin Airport in the capital. This airport is being served by most major normal and low-budget airlines. There is also the Warsaw/Modlin Mazovia Airport, located close to Warsaw. This airport operates low-budget airlines.
The journey takes about 2 hours and 15 minutes from the Warsaw Central Station whereas from Chopin Airport to Warsaw Central/West/East station there are trains runnings about 20/25/30 minutes. From Warsaw/Modlin Mazovia Airport it takes to travel by train more than 3h as you need to go to Warsaw East train station and then direction to Bialystok.
There is a direct coach connection from the Warsaw Chopin Airport operated by Plus Bus, Zak Express or PKS Express. For timetables and prices, see http://zakexpress.pl/ or https://plusbus.pl/rozklad.php