Because of the likelihood of a resident's bodily fluids being on or in their clothing or bed linens, what type of safety precautions should you take?

First, always wash your hands after touching the linen or clothing. Washing hand can prevent the bodily fluid spread to health care provider or other patients. 
After that make sure that the linen and clothing are washed frequently. The washing procedure should be able to kill pathogens so the worker in laundry can be safe.