I've got a swaddlebees bag instead of a bin, also a wonderoos one as I like to separate my wraps from inserts for washing. The swadlebees would be big enough for twins no prob, it holds more than a full load for my machine & theres one for sale for £5 on mamigreen.co.uk at the mo in the bargains section. The wonderoo is still pretty large but not as big & the cord gets stuck on the PUL so not as good IMO.
I also think putting a kitchen towel with a drop or 2 of tea tree will help contain smells & is antibacterial too
hope that helps