A Scrub and a Wax
Clean Grout with a Bleach Pen
For really mildewed grout, you may need a second application, and it can help to gently scrub the bleach into the grout with a toothbrush before allowing it to work for 10 minutes. Make sure to run the fan in the bathroom and to avoid skin contact. This method is best for light or white grout. If you have colored grout, test a small area first. It might fade.
Instead of trying to find a bleach pen at the store, the cleaning solution to grout might already be in the bathroom.