When a place is bustling, it is full of people moving around and doing things. A bustling market, a bustling kitchen, a bustling street: you hear voices, you see motion, nobody is standing still. It is a lively, warm kind of busy, not the heavy, stressed kind. We mostly use it about places, or about a time of day in a place (“the café is bustling at lunch”). You can say a place is bustling with people or with activity. It comes from the verb bustle, to move about in a busy way. Ordinary English — not slang, not especially formal.