shower mold/mildew

anybody have any tips on how to safely and naturally remove this from the grout lines in my tiled shower (the tile is old in our rental (circa 60's I think)- so the grout holds mold and mildew and it just keeps coming back no matter what I do or spray.) The only thing I've found that works is straight bleach - but the mold keeps coming back, and the bleach flat out makes me have a headache and sick to my stomach - I can't stand to be near it - but I also can't stand a moldy shower. I purchased the Bac-out product which has helped a little - I've sprayed and let it sit and soak in twice - scrubbing doesn't seem to help because it's down in the porus surface. Is there another product anybody would suggest for this?

Thanks
Jen