https://pachamamahome.com/cabanaconde.htm#horariodebus : here you will find the public bus schedule between Arequipa and the Colca Canyon. You can stay overnight in Cabanaconde.Edited: 1 year ago
Depending on what day you are traveling the 4M bus goes from Cusco to Chivay three times a week https://www.busperu4m.com/routes.html#cusco-to-chivay
Do you want to go hiking in the canyon? Do a Colca Canyon trek? Or do you want a tour that goes to the Colca Valley and the Cruz del Condor which is the start of the actual canyon? The trek also goes to the valley and the Cruz del Condor but continues to Cabanaconde to hike down into the canyon.
You can book 2 day tours and treks in Arequipa. The 2 day trek would still leave at 3 am but the two day tour leaves around 7-8 am.