A device to package a sterile bulk product, particularly, a dermocosmetic or galenic preparation, into a container. A sterile enclosure of the device includes a hopper containing the bulk product. The hopper includes in an axial direction, a cylindrical reservoir part and a pouring part connected to the cylindrical part. A transfer device transports the container under the hopper to fill the container in a filling zone. A blower provides ultra-filtered air from the ceiling to the floor of the enclosure, to produce a protective flow of air around the filling zone. The axis of the pouring part with an asymmetrical conical shape is not in line with the axis of the reservoir part such that the pouring opening is shifted towards the outer wall of the reservoir.