Don't ever believe you are going to get good buses out of La Paz or direct bus to Arequipa.
Buses normally stop at Puno bus station and changed bus. Puno bus station is huge and tidy, safe too.
So, buy your ticket up to Puno and get the bus ticket from Puno to where ever you want to go in Peru. It is cheaper to buy the ticket in Puno, then buying it from La Paz. It works that way.
Some more, most connecting buses that the agency buy are not good. The bus normally made a lot stop and pick up local, make it easy target for hijacking.