Charles Reed Bishop, Hawai'i philanthropist and co-founder of Kamehameha Schools and First Hawaiian Bank, built the museum in memory of his late wife Bernice Pauahi Bishop. She was the last direct descendant princess of the Kamehameha Dynasty that ruled over the Kingdom of Hawai'i since 1810. Bishop had originally intended the museum to house family heirlooms passed down to him through the royal lineage of his wife.
The museum was built on the original boys campus of Kamehameha Schools, an institution created to benefit native Hawaiian children as outlined in the Princess' last will and testament. In 1898, Bishop constructed Hawaiian Hall and Polynesian Hall in the Victorian architectural style. The Pacific Commercial Advertiser newspaper dubbed the buildings as "the noblest buildings of Honolulu." Both Hawaiian Hall and Polynesian Hall stand today and have been listed on the National Register of Historic Places. Hawaiian Hall is home to a complete sperm whale skeleton with paper mache body suspended above the central gallery. Along the walls are prized koa wood display cases worth more than the original Bishop Museum buildings. It is also home to The Hawaiian Royal Regalia, including the Hawaiian Royal Crowns and the Consorts Crown.
In 1940, Kamehameha Schools moved to its new campus in Kapalama. This allowed the museum to expand. Most school structures were razed and new museum facilities were constructed. By the late 1980s, the Bishop Museum had become the largest natural and cultural history institution in the Pacific Rim.
In 1988, construction of the Castle Memorial Building was begun. Dedicated on January 13, 1990, Castle Memorial Building houses all the major traveling exhibits that come to the Bishop Museum from institutions around the world.
The Richard T. Mamiya Science Adventure Center opened in November, 2005. The building is designed as a learning center for children, and includes many interactive exhibits focused on marine science, volcanology, and related sciences.
The Bishop Museum also administers the Hawaii Maritime Center in downtown Honolulu. Built on a former private pier of Honolulu Harbor for the royal family, the center is the premier maritime museum in the Pacific Rim with artifacts in relation to the Pacific whaling industry and the Hawai'i steamship industry. On the Big Island of Hawai'i, the Bishop Museum administers the Amy B.H. Greenwell Ethnobotanical Garden, specializing in indigenous Hawaiian plant life.
The Secretariat of the Pacific Science Association (PSA), an independent regional, non-governmental, scholarly organization that seeks to advance science and technology in support of sustainable development in the Asia-Pacific, has been based at Bishop Museum since PSA's founding in 1920.