First, it's Bailey, not Baily and definitely not Baileys. Second, you don't hike along Bailey (it's a town and the name of a section). You'd hike along the North Fork of the South Platte River.
So, there's no camping at the Bailey takeout. And there is a ranger residence, so I wouldn't try it. It could definitely be a good night hike from there. Dogs have to have leashes - willa got a ticket when she ran and jumped into the ranger's truck. There's camping not far near buffalo creek, but I don't have any better details or beta.