Bellerophon didn't ride Pegasus

The apparatus criticus being:

From wiki:

"The Lycian seer Polyeidos told Bellerophon that he would have need of Pegasus. To obtain the services of the untamed winged horse, Polyeidos told Bellerophon to sleep in the temple of Athena. While Bellerophon slept, he dreamed that Athena set a golden bridle beside him, saying "Sleepest thou, prince of the house of Aiolos? Come, take this charm for the steed and show it to the Tamer thy father as thou makest sacrifice to him of a white bull."

(Kerenyi 1959, quoting Apollodorus Mythographus, 2.7.4.).

"It was there when he awoke. Bellerophon had to approach Pegasus while it drank from a well; Polyeidos told him which well—the never-failing Pirene on the citadel of Corinth, the city of Bellerophon's birth. Other accounts say that Athena brought Pegasus already tamed and bridled, or that Poseidon the horse-tamer, secretly the father of Bellerophon, brought Pegasus, as Pausanias understood.[12] Bellerophon mounted his steed and flew off to where the Chimera was said to dwell."

(Pausanias, Description of Greece 1.4.6.)