If you're in a major rush to get there, Grupo de Transporte Aéreo fly to Concepción from Asunción at 6am Wednesday, with an early-afternoon return on the same day if there is demand.
The most traditional (but not the most comfortable) way to access Concepción is by riverboat. Typically these are cargo boats that lack basic services (including a toilet) and you'll need to take your own food and drink. Boats heading upriver to Vallemí (65,000G, 30 hours) or as far as Bahía Negra (110,000G, three days) include the Aquidabán (departs 11am Tuesday, returns Friday) and the erratic Guaraní, which leaves fortnightly on Monday afternoons but goes only as far as Fuerte Olimpo via Vallemí, and returns Thursday. Check schedules and boats in advance (0331-24-2435); they change frequently.
The bus terminal is eight blocks north of the center.
For Asunción (90,000G, 4½ to six hours), La Santaniana and La Concepciónera offer the best service. Several services head to Pedro Juan Caballero (35,000G, four hours) and Filadelfia (100,000G, six hours). There are daily departures with NASA at 12:30pm and 8pm to Ciudad del Este (100,000G, nine hours).