From Yaviza I took a boat to El Real for $10 US, on the way back though they charge me $5.00 US. This is a short one hour ride though beautiful vegetation.
Other routes deeper into the Darien jungle: Prices of boats (motor canoes) from El Real to Boca de Coup ($100 US), from El Real to Pucuro ($100 US w/ Kunas), and to Paya for ($150 US).
The bus from Panama to Meteti ($9 US) took about 7 hours in good weather. From Meteti to Yaviza, the chiva (4x4 truck, $5 US) took 2.5 hours through a dry road under good weather, but then it took 5 hours on the way back through the same rainy muddy road. On the dry season, you may be lucky and find a direct bus all the way to Yaviza :).