People in Pamplona rent out apartments/rooms in their apartments, but it can be quite pricey and they fill up fast. If you choose to sleep in a park or tent bring a sleeping bag because it gets chilly there at night. I’d also consider staying in San Sebastian and taking a bus down to Pamplona. You could take the bus down just for the running in the morning and then head back to San Sebastian, or take it down the night before, party overnight, run with the bulls, then bus back.