 Bøyesen was elected mayor of Porsgrund municipality for the years 1843, 1844 and 1846, having first been elected to the municipal council in 1842.Bøyesen was then elected to the Norwegian Parliament in 1845, 1854, 1857 and 1859/60, representing the constituency Porsgrund.In 1848 he had been elected deputy representative from the constituency "Porsgrund og Brevig".