Bowman (also know as Bow-man) was the eccentric archer from the planet Angor. As the rest of his team, the Champions of Angor/Assemblers, he is a homage/parody to Marvel's Hawkeye.
Previously only know throught flashback cameos, Bow-Man was really explored in Justice League Quarterly #3 - When You Wish... He was presented as a guy with several quirks and psychological problems. Also must noted than his physical appearance in the JLQ chapter (by McKone) was different from the original design in the flashbacks (design by Sears). He died along with most all the population of Angor.
After 52, in the miniseries Lord Havok, he was reinvented as the Secretary of Security for the President, Americommando, in a more darker mood, as the rest of Angor/earth-8. He was killed during the final assault against Lord Havok.
A new archer know as Deadeye appeared in Multiversity, as member of the Retaliators. At difference of the original Bow-man his skin is blue. His origins are unknown.