The Duchess of Sussex, 38, let the cute monicker slip as she and Prince Harry prepared to meet Archbishop Desmond Tutu for tea in Cape Town.
A video of the moment was shared on their Sussex Royal Instagram page's Stories yesterday.
As the couple walked down a corridor on their way to greet the cleric, with Meghan cradling the four-month-old in her arms, Harry excitedly told his son: 'You get to meet Arch, you get to meet Arch!'
As the youngster grinned at his father, Meghan is heard saying: 'Oh Bubba.'
Later on, when the couple met the South African human rights activist and his daughter, Thandeka Tutu-Gxashe, Meghan was reportedly heard using the nickname again.
Meghan told her son: 'Say hello! Hello, hi,' before realising Archie was drooling, to which she exclaimed: 'Oh, Bubba!', People reports.
In America, Bubba is usually used as a term of endearment derived from 'brother', mainly given to boys. In Australia and New Zealand it's commonly used as a noun to refer affectionately to a baby.
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