The most popular route from Buenos Aires to Punta del Este is by ferry. All routes to Punta del Este from Buenos Aires connect by bus in either Colonia or Montevideo (AR$222), depending on the time of day you are leaving. Check the ferry schedule ahead of time. Punta del Este is two hours by bus outside of Montevideo or  four hours from Colonia. Buquebus (www.buquebus.com)  also occasionally offers specials on its website.
That said, some people prefer to fly. Pluna, Aerolíneas and Lapa run daily flights from Buenos Aires to Punta del Este (40 minutes) direct, but only during the tourist season from late December to late January.
For those on a tight budget: a bus from Retiro Terminal in Buenos Aires takes 10 hours and costs $30. Changes can also be made in Montevideo.