As far as I know there aren’t any campgrounds in the city limits. There is an RV park but I don’t think they have tent camping: https://www.sunoutdoors.com/oregon/sun-outdoors-bend
Your best bet would be Tumalo State Park, La Pine State Park, or if you want to disperse camp check out the Badlands east of Bend and you can camp for free. That may be your best bet especially because most sites get reserved ahead of time at most of these popular campgrounds.
sunoutdoors.com
RV Resort in Bend, OR – Sun Outdoors Bend
Plan your next family camping vacation at our scenic Bend resort with RV sites, vacation rentals, event space, pool, and activities like pickleball and tennis.