The physical distance is not as important as the work practices that keep clean and soiled items separate. Soiled linen containers need to be labeled and use for this sole purpose. A liner can help keep the container clean but is not required. The container must be kept clean by regular, scheduled cleaning. The soiled linen container can be brought to the room to decrease the distance linen is carried.
Some facilities require that soiled linens be bagged in the room and then brought to the container.
Personal clothing hampers can be stored in the residents room and emptied regularly. Infectious agents such as MRSA and VRE are inactivated during the regular laundring process. No special linen handling is requied. Your facility's infection control plan should included ways to prevent worker illness in the laundry.