In some countries there was, maybe still is, an old tradition of blessing bread and sharing it after mass. This was very common in France. From this article (written in the early 20th c.):
The little loaves or cakes of bread which received a special benediction and were then sent by bishops and priests to others, as gifts in sign of fraternal affection and ecclesiastical communion were also called eulogiae. Persons to whom the eulogia was refused were considered outside the communion of the faithful, and thus bishops sometimes sent it to an excommunicated person to indicate that the censure had been removed. Later, when the faithful no longer furnished the altar-bread, a custom arose of bringing bread to the church for the special purpose of having it blessed and distributed among those present as token of mutual love and union, and this custom still exists in the Western Church, especially in France. This blessed bread was called panis benedictus, panis lustratus, panis lustralis, and is now known in France as pain bénit. It differs from the eulogia mentioned above, because it is not a part of the oblation from which the particle to be consecrated in the Mass is selected, but rather is common bread which receives a special benediction. In many places it is the custom for each family in turn to present the bread on Sundays and feast days, while in other places only the wealthier families furnish it. Generally the bread is presented with some solemnity at the Offertory of the parochial Mass, and the priest blesses it before the Oblation of the Host and Chalice, but different customs exist in different dioceses. The prayer ordinarily used for the blessing is the first or second: benedictio panis printed in the Roman missal and ritual.
It sounds like St. Bernadette would have been familiar with this tradition. A similar tradition exists in the Byzantine Rite.