Bayard is a city in Grant County, New Mexico, United States. It is near Santa Rita, east of Silver City. The population was 2,116 at the 2020 …Bayard is a city in Grant County, New Mexico, United States. It is near Santa Rita, east of Silver City. The population was 2,116 at the 2020 census. It is located in east-central Grant County. According to the United States Census Bureau, the town has a total area of 0.95 square miles, all land. The city is in the valley of Whitewater Creek, a seasonal south-flowing tributary of the Mimbres River.