By public transport its really easy to reach the hostel in an hour (in case of traffic jam it could be a bit more). Single ticket costs 350 HUF (around 1,1 EUR) and it can be bought at the bus stops from a machine.
By taxi the price can be between 20-30, depends on taxi driver. In case of need, airport shuttle can be provided by the hostel. Please ask for more details in private message!