Bullards Bar is a former settlement in Yuba County, California, United States. It is located on the North Yuba River 6 miles southeast of Ch…Bullards Bar is a former settlement in Yuba County, California, United States. It is located on the North Yuba River 6 miles southeast of Challenge, at an elevation of 1909 feet. Bullards Bar was inundated by Bullards Bar Reservoir. A post office operated at Bullards Bar from 1866 to 1914. The name is in honor of Dr. Bullard, an early miner here.