he was a member of the virginia house of delegates from 1787 to 1789, and the virginia senate from 1794 to 1805. he was unsuccessful in contesting the election of john clopton to the united states house of representatives in 1794, but was later elected as a democratic-republican in 1804, serving from 1805 to 1813. there, bassett served as chairman of the committee on claims and of the committee on revisal and unfinished business from 1811 to 1813. he was an unsuccessful candidate for reelection in 1812, but was elected again in 1814, serving from 1815 to 1819. bassett then returned to the house of delegates, serving from 1819 to 1821, and returned to the united states house a third time, serving from 1821 to 1829 as a democratic-republican, crawford republican and jacksonian. he was unsuccessful for reelection, and died on february 26, 1841 in new kent county, virginia. he was interred at the eltham plantation, in eltham, virginia, in new kent county.