Everybody’s piercing closes at a different rate. It could be anywhere from a few weeks to a couple of months for it to be closed enough to re-pierce in the same spot.
I’d suggest a glass retainer for keeping it hidden at work. They’re pretty discreet. Fused quartz glass, lead-free borosilicate, and lead-free soda-lime glass are inert and considered safe for initial piercings. They can also be sterilized in an autoclave.