"bustling by" is correct and usable in written English.
You could use it to describe a person quickly moving through a busy area, such as: The lively city street was full of people bustling by.
As we sipped, the townswomen -- dressed in traditional salvar (baggy pants) -- came bustling by with their crew-cut boys and pig-tailed girls, all anxious to buy book bags and shoes since school throughout Turkey would begin the following Monday.
"Then, on the first day I was clearly pregnant, she comes bustling by with four cups of coffee in her hands and asks, 'So what are you having?' I thought she meant what kind of eggs.
So were the bars and coffee shops; the Men's Room, the Midnight Sun, and even the "gay" Starbucks, on Eighteenth Street, were all bustling by 8 p.m., and a small crowd had begun drifting into Magnet.
Start with Downtown, bustling by day, much less so at night; people work there but don't play there, and Centennial Olympic Park, created for the 1996 games, has not quite pulled the area together the way the city fathers had hoped.
We relish the excitement of Mercedes Benz Fashion Week Fall 2012, as a dizzying, somewhat dyslexic time, when we bundle up in our winter's wool and fur, while bustling by the boutiques on Madison and Fifth Avenue, brimming with the bright fashions of early spring and resort, simultaneously scurrying to survey the styles sashaying the runways for next fall.
A slip of a fishing village with nothing in it but a post office, a pub and the Lugger, it makes St. Mawes look positively bustling by contrast.
I held open the door and they bustled by.
Also, some viewers, hustled and bustled by the action, may find it all too much.
Outside the Hilton Hotel in Buenos Aires, the colourful life of the Argentinian capital bustles by.
In a little more than an hour seven pieces surged and bustled by in a near-seamless flow.
As the giant waves roll in and out, they hypnotize any sentient being who might be trying to bustle by.
