Numerous buses and minibuses ply the stretch from Bicaz to Gheorgheni (13 lei, 1½ hours) throughout the day, passing through the gorges and stopping (on request) at Lacu Roşu. If you're trying to catch a bus out of Lacu Roşu, hail down passing buses on the main road, near the lakefront. Buy your ticket from the driver.
Three daily trains connect Bicaz and Piatra Neamţ (5 lei, 30 minutes). Note the train does not pass through the gorges to Lacu Roşu and Gheorgheni.