Taxis are cheap and safe in Natal, for example, a short drive from Ponta Negra to Natal Shopping (about 10 km) costs 10 R$. Prices are rising slightly in the evening and also in the high season (July, Dec, Jan and Feb). You can often negotiate a bit about the price in advance, especially if you have to go to multiple places.
By bus you can get anywhere. The local bus certainly has its charm, but is hardly comfortable for longer distances. The bus station in Natal is called ‘Rodoviaria’ and is located in the Centre of the city. From here you can travel to almost all destinations in Brazil. Especially on popular routes this is a superclass bus (VIP) with airconditioning. These buses drive mostly at night and offer good service. Bus tickets are out there for sale.
As the salary is very low in Brazil, tips are always welcome. To baggage personnel or room girls you can give a tip of about 2 or 3 R$. When you are satisfied with your guide or driver you can give him about 5-10 R$ a person after a day tour. The driver who brings you to the airport or hotel and that carries your bags for you; you can give about 2 or 3 R$ a person. In the middle and higher class restaurants it is customary to leave a tip of 5-10 percent of the price.