A private local bus operator has proposed a double-decker bus service to carry commuters between North Station, South Station and South Boston, touting it as a relatively inexpensive link between the city’s two train hubs.

Under a proposal submitted to the MBTA last month, A Yankee Line Inc., which is based in South Boston, would operate the service using subsidies from the MBTA. The company would buy, own and maintain the buses, with the MBTA pocketing any fare revenue greater than the service’s…