In many cases, Cleopatra herself, similarly disguised, would go out with him.

On these excursions Antony would take pleasure in involving himself in all sorts of difficulties and dangers--in street riots, drunken brawls, and desperate quarrels with the populace--all for Cleopatra's amusement and his own.
Stories of these adventures would circulate afterward among the people, some of whom would admire the free and jovial character of their eccentric visitor, and others would despise him as a prince degrading himself to the level of a brute.
Some of the amusements and pleasures which Antony and Cleopatra pursued were innocent in themselves, though wholly unworthy to be made the serious business of life by personages on whom such exalted duties rightfully devolved.

They made various excursions upon the Nile, and arranged parties of pleasure to go out on the water in the harbor, and to various rural retreats in the environs of the city.

Once they went out on a fishing-party, in boats, in the port.

Antony was unsuccessful; and feeling chagrined that Cleopatra should witness his ill-luck, he made a secret arrangement with some of the fishermen to dive down, where they could do so unobserved, and fasten fishes to his hook under the water.