I'm in the process of re grouting a shower floor. I've removed loose grout with a grout saw and ready to apply new grout. Question - Most of the grout is still in good shape and very little was removed (mostly only edge spots). Along the edge is mold. I've attempted to use cleaners to remove the mold not removed using the saw. Should I apply new white grout over dark covered mold? If not what should I do with these dark mold spots so there don't re appear? Is there anything additional I should consider when re grouting?

Use bleach on mold and clean with water/soap complete, let dry and grout