It isn't an item you can equip to a pokemon, it's just a key item
that's always active.
It allows you to send more pokemon out on rumble missions, but they
can be whatever pokemon you want them to be, they do not have to be
the same ones all the time.
There are ways to obtain more explorer bags such as buying them
from mall, your Pokémon that you sent on rumble missions might find
one, and also completing your badge sets- this gets you a bag for
every set you complete.
So keep sending your pokemon on rumble missions and you'll might
find one