The Bradbury-class was a type of Federation transport of an experimental class in service to Starfleet in the 24th century. It was named for author Ray Bradbury. (ST reference: The Star Trek Encyclopedia, ST website: StarTrek.com)
The Ship Recognition Manual, Volume 1: The Ships of Starfleet, an ebook released by Last Unicorn Games after losing their Star Trek license, states that the Bradbury-class was a type of heavy cruiser which entered service in 2362. In addition to the USS Bradbury, it also lists the USS Charthev (NCC-74120), USS Joyce (NCC-73097), USS Tolkien (NCC-73112) and the USS Twarel (NCC-73113) as Bradbury-class starships.
The Dominion War Sourcebook: The Fires of Armageddon, also published by LUG after losing their license, also lists the USS Damara (NCC-70359) and USS Grigni (NCC-64967) as Bradbury-class starships.