Bread from meat meal at dairy meal

It is forbidden to eat the bread from a meat meal at a dairy meal (Shulchan Aruch, Ch.9, Siman 4) due to the concern that the bread was touched and meat remnants remained on it, and afterwards if eaten at a dairy meal, it means that meat and dairy were eaten together. If however, the bread was in a plastic bag, and at the beginning of the meal, each diner took out a few pieces for himself, and then the bread in the bag remained clean, it is permissible, as long as the bread that was on the table is not included.