I feel like I’m constantly buying pine shavings, maybe I’m not putting in enough initially?
It's supposed to break down as the poop and the bedding material compost. Can you get wood chips? They'll last longer. You can use any compost brown in there and a mix of different sizes and materials makes for better aeration and draining.
Often a landscape company will be willing to dump a truckload of chips on your property -- that way they don't have to pay to dispose of it. The chips need to be aged for a while before putting them in the run, but if you have space it's free.