'come bustling' is a correct and usable phrase in written English.
It is used to describe a situation in which somebody is moving energetically, often as part of a busy or crowded scene. For example, 'The street was bustling with life, as shoppers came bustling in and out of the stores.'.
Nodding excitedly, he called for his partner, who came bustling out of the shop and into the street.
Dr. Dimitrov soon came bustling up, and led us through a park full of statues and inoperative fountains.
Shortly after she comes bustling onstage, radiating maternal warmth, Ms. Blythe blows the audience away with her astoundingly lush voice, leading the exuberant "June Is Bustin' Out All Over".
I remember this woman came bustling out of a doorway when I first got there - she reminded me of my mum, which didn't help - and said, "Just done my second... better go and rinse my mouth out".
And then she swung it upwards and it cracked against his jaw and Hugo - shocked now, pitching back numbly (hurt like hell later) - took the full force and fell from view as Piers came bustling up and cried What the hell and Christ, Jeremy - is this bitch with you?
So Hoover comes bustling out, and Mac accuses him of trying to entrap him.
First night in the Tunis hotel, a player comes bustling down to supper, enthusing "Great to be in Africa, eh, boss?" to be corrected sternly by Gordon: "Don't be daft, laddie, this isn't Africa, it's Tunisia".
"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.
By now he was approaching the oche like a pear-shaped medium pacer coming bustling in to bowl, sealing a 4-2 set lead with a thrilling double 18 finish.
Shortly after 19 00, Gunther Schabowski came bustling in and sat down in front of the microphones.
