Bert grew up in a fairly wealthy household, and though he was an only child, his parents didn’t have time for him and hired a nanny. Thus Bert meets Mary for the first time. Though she appears somewhat strict and no nonsense, Bert thinks she’s one of the lovliest people he’s ever met, and develops a childhood adoration for her. He does everything for her exactly as he’s told, though sometimes he acts out just to get her attention (this accounts for his goofy behavior around her as an adult).
Eventually it came time for Mary to leave Bert for other children, and his life was never really the same after she left. His parents fell on hard times, and Bert had to take up odd jobs to help support them.
Imagine his surprise and delight when, years later, he sees his childhood idol floating down from the clouds to fulfill her eternal role as nanny.
The reason why he recognizes her is because of his deep love for her, and the countless other children she looked after pass her in the streets without a hint of recognition because they have stopped believing in the magic Bert so desperately clung to as a boy.
Even now, Bert is still unbelievably devoted to Mary Poppins, and waits patiently, because he knows no matter where she goes, she will always come back London…. and him.