we use bbh's too we have a 16 month old and a baby on the way who will be in them too. we just have a large target brand bag we use it for daycare too. It fits over nay single pram and nay double pram as we have both, i cant see why it wont work when bub is here for us as for daycare we put 5 magicals in it large and about 10 wipes and 2 out fits so for shopping trip i would take 2 magicals in each size newborn and large and 4 out fits 3 for bub and 1 for toddler and about 10 cloth wipes and the bag to put wet nappies in that would all fit well and a small bottle bag.