Does Bruce Wayne carry a suit with him?

Batman only goes out at night. In this very good movie, Bruce Wayne has no social life, so he's always home and close to the batcave where puts on his batsuit.

I think it was implied he was changing. It's a bit silly to think of him lugging that armour around in that backpack, but I kinda dug the comic book logic of it.

I feel like he's riding around on the bike wearing the boots and the "undersuit" and then he has the armoured bits, gauntlets, belt, cape, and cowl in his pack.