What to expect
Start the booking with the day around the journey, not the seat. Write down your departure address in Arequipa and your accommodation in Chivay. Then ask what route the operator uses, where it stops and how you complete the final stretch. That makes the offers comparable.
How it fits into a journey
Use this journey to reach your Chivay accommodation. Arrange the return to Arequipa separately; do not assume a one-way trip also organises an onward connection to Puno.