Buses 306 and 813 (the same ones you take to the airport) also pass the bus station; get on either at Praça da Matriz or on Av Gétulio Vargas. The bus station is small and easy to miss, so be sure to keep your eyes peeled.
You can catch the same buses back into town. Leaving the bus station, use the pedestrian bridge to cross Rua Recife and turn left along the busy street on the far side of the gas station there. The bus stop is 100m further along, on the far side of the street.
A taxi between the bus station and the center costs R$35 to R$40.