I've not had a PICC or even an IV for treatments, but I did find this - it's for children with PICC's, but you'll get the idea:
"When can my child bathe or shower after the tunneled central line is removed?"
"Your child shouldn’t take a shower or bath for 48 hours, until you have removed the gauze and clear tape unless specifically allowed by your doctor. After that baths and showers are OK. If showering, your child should face away from the spray so water does not hit the site directly. If taking a bath, your child should keep the site above the water. Once the steri-strips have fallen off your child may shower or bathe as usual. "
/medicine.yale.edu/surgery/pediatric/care/information/outpatient/central.aspxI hope that helps some!!