If you know you're going to be buying a lot of wine, ask the first winery for a 12-shipper (box with 12 compartments) (or sometimes they have 8- or 9-shippers). They'll be happy to give you one if you're buying a couple of bottles from them. Then you can stash the rest of the bottles in there as you go, all in one box. (If it's hot remember to keep it in your air conditioned car, not the trunk.)
If you're only buying a bottle or two, don't worry about it--they'll also have little handled boxes for 2 or 3 bottles.