Bayne became a lieutenant on 5 April 1749; in 1755 he served in that rank on board HMS Torbay, in North American waters, with Admiral Edward Boscawen, and in November 1756 was advanced to the command of a sloop of war.

Owing to the faulty system of tactics then in vogue and almost compulsory, the Alfred had no active share in either of these battles, the circumstances of which were afterwards much discussed.

On returning to the West Indies the Alfred was with Sir Samuel Hood at the Battle of Saint Kitts, where she accidentally fouled the frigate HMS Nymphe, cutting her down to the water, and losing her own bowsprit.

Bayne quickly refitted his ship and resumed his station in the line, which won him credit, as did his distinguished conduct in the battle.

To his memory, jointly with that of Captains William Blair and Lord Robert Manners, who were killed in the battle three days later, a national monument was placed in Westminster Abbey.