This phase III trial compares the effect of olaparib for one year versus two years, with or without bevacizumab, for the treatment of BRCA 1/2 mutated or homologous recombination deficient stage III or IV ovarian cancer. Olaparib is a polyadenosine 5'-diphosphoribose polymerase (PARP) enzyme inhibitor and may stop the growth of tumor cells by blocking some of the enzymes needed for cell growth. Bevacizumab is in a class of medications called antiangiogenic agents. It works by stopping the formation of blood vessels that bring oxygen and nutrients to tumor. This may slow the growth and spread of tumor. Giving olaparib for one year with or without bevacizumab may be effective in treating patients with BRCA 1/2 mutated or homologous recombination deficient stage III or IV ovarian cancer, when compared to two years of olaparib.