Bout, n.
Etymology: [A different spelling and application of bought bend.]
1. As much of an action as is performed at one time; a going and returning, as of workmen in reaping, mowing, etc.; a turn; a round. In notes with many a winding bout Of linked sweetness long drawn out. Milton. The prince . . . has taken me in his train, so that I am in no danger of starving for this bout. Goldsmith.
2. A conflict; contest; attempt; trial; a set-to at anything; as, a fencing bout; a drinking bout. The gentleman will, for his honor's sake, have one bout with you; he can not by the duello avoid it. Shak.
Shades of meaning
Fernald has no entry of its own for bout; he lists it under battle.
He lists it without comment; the entries above explain its neighbors.