There is no Bates Motel in Bates, Arkansas, but the town does have an abandoned school, a two-story brick building built in 1905 and abandoned in 1965. This site has about 120 pictures:
Wikipedia sums up Bates in only a few words: “Bates is an unincorporated community in Scott County, Arkansas, United States. It is the location or nearest community of Bates School, at 1074 Bates School Rd., which is listed on the U.S. National Register of Historic Places.”
Arkansas Hometown Locater terms Bates “a minor civil division of Scott County.”
Trip Advisor lists “10 best motels near Bates.” The closest motels are almost 20 miles away, in Poteau, Oklahoma.
Hometown USA lists a link to census data, but the link is a 404 error.
Roadside Thoughts has this: “As far as we can tell, Bates has not been included in past Census counts, so there is no population information for this community.”
Here is a link to a satellite image of Bates:
Granted, there are only a few houses, most north of Arkansas Highway 28. The Poteau River meanders where it will, south of town. The Poteau starts in Scott County and flows into Oklahoma until entering the Arkansas River near Fort Smith, Arkansas.