I heard Jabir bin Abdullah being asked about riding the sacrificial animal. He said, "I heard the Prophet ﷺ say, 'Ride it in a reasonable manner when you have no other choice, until you find another mount.'"
سمعت جابر بن عبد الله سئل عن ركوب الهدي، فقال: سمعت النبي ﷺ يقول: اركبها بالمعروف إذا ألجئت إليها حتى تجد ظهرا.
Muslim narrated it in Hajj (1324) from Muhammad bin Hatim, who said, Yahya bin Saeed narrated to us, from Ibn Jurayj, who said, Abu Zubayr informed me, and he related it.His saying, "until a specified time" [reference not given in source] means until a determined time, which is her arrival at Makkah and her being sacrificed at Mina or elsewhere in the valleys of Makkah.