Baneasa is much closer to the city centre (perhaps uniquely in Europe for a budget-airline dominated airport), and two busses, 131 and 335 stop outside, terminating at Piata Romana. You will need to buy a Multiplu Card (costing 1.60 lei) and load it up with credit: 1.30 lei is needed for each journey, and you can load the card with anything from two to ten journeys.There is a ticket booth to do all this next to the bus stop. The new express route 780 to Gara de Nord also now stops outside.
Note that Baneasa is a tiny airport and two planes landing simultaneously can bring the place to a standstill. There is a cashpoint, but it often runs out of money, and the currency exchange is a rip-off.
Taxis wait outside, but make sure you take one belonging to a trusted Bucharest taxi company (click on Taxis, left). The fare to town should cost no more than 25.00 lei, and take 15 minutes depending on traffic.