After Cilan left the Gym, Burgundy came back and earned her Badge, then found her way to the mall before Cilan.
Maybe she can teleport, or has super speed? Or maybe Cilan and co. are just lazy.
I think its a known fact that everyone travels faster than Ash and co.
But, besides that, Burgundy certainly does have super speed. Did you see the way she zoomed off at the end of the episode? She's a girl full of determination and a thirst for revenge. Nothing can stop (or slow) her.
Burgundy is a species of her own kind. It's pretty obvious that, yeah, Ash is a very slow and easily distracted traveller, but Burgundy has magical connoisseur powers on her side.