Arriva Derby is a bus operator in Derby. It is a subsidiary of Arriva Midlands.

In March 1880, the Derby Tramways Company commenced operating horse-drawn trams between Market Place and Derby railway station. The Derby Corporation Tramways, &c. Act 1899 (62 & 63 Vict. c. cxciii) saw the Derby Corporation take over the tram lines in November 1899. Between 1903 and 1907 the network was extended and electrified.

In May 1917, a Tilling-Stevens petrol-electric bus entered service. A second entered service in 1920, but both were replaced with motor buses in 1924. Between January 1932 and July 1934, Derby's trams were replaced by trolleybuses. Motor buses continued to operate alongside the trolleybuses until the network began to be closed in the 1960s, with the last running on 9 September 1967.

In December 1973, Derby Corporation purchased Blue Bus Services of Willington. In 1974, Derby Corporation was renamed Derby Borough Transport and later became Derby City Transport when Derby was granted city status in 1977.

To comply with the Transport Act 1985 and ensuing deregulation of bus services from 26 October 1986, the assets of Derby City Transport were transferred to a new legal entity, Derby City Transport Limited, in October 1986. Following deregulation, Derby City Transport Limited was placed up for sale by Derby City Council in January 1989, and in the intervening period, saw minibus competition from Midland Red North, formed from the split of National Bus Company subsidiary Midland Red and operating locally under the 'Mercian' brand.

Following six months of negotiations between Derby City Council and company employees, Derby City Transport was sold for over £3 million (equivalent to £7,938,000 in 2025) in July 1989 to a consortium consisting 75% of an employee buyout team and 25% Luton & District, beating a management buyout bid as well as interest from Trent Buses, Midland Red, Stevensons of Uttoxeter and Go-Ahead Northern.

Derby City Transport took over competitor Camms of Nottingham's bus operations in 1993 after the latter decided to return solely to coaching work, altering the timings of Camms services in Derby to reduce duplication as well as moving 15 buses from Derby to Nottingham in order to operate Camms' school and local authority contract services. Having revived the Blue Bus Services name for the company's coaching arm in 1984, Derby City Transport adopted the Blue Bus name for the entire bus fleet in January 1994, with buses being painted into a two-tone blue livery with white striping.

In July 1994, Derby City Transport was sold to British Bus, who by then had gained a 25% stake in the company through their earlier purchase of Luton & District. In 1995, Derby City Transport's Blue Bus identity was replaced by a new City Rider brand, with new Scania N113DRB double-decker buses and Mercedes-Benz 711D minibuses adopting a yellow, red and blue livery, drivers being issued with new uniforms matching the livery, and more frequent bus services being operated.