Depends on the size of the run, the health of the turf, the amount of rain, and other factors.
It took my 7 chicks months to start creating bare spots in their pen last summer, but my pen is over 600 square feet (100 feet of Premier 1 electric poultry netting), and I kept moving the posts to expose fresh ground every couple weeks.
But now, after about 10 months, they can destroy grass a lot faster than it can grow when I expose new ground and the core of their area has been covered in pine straw since November.
I'd put down bedding when the run seems to need it -- when the ground looks bare and torn up or when you just start to notice a potential mud or odor problem starting.