craftgrrl | question about dyeing fabric

Sorry for the text only post, but I have a quick question that I'm sure someone here could give me insight on. I accidentally got bleach on one of my work shirts; not a whole lot (I likely just brushed up against a surface I'd recently sanitized, so there's a big pinkish area across the front), but it's noticeable, so I figured I'd try dyeing it so I can still wear it. It's black, so I'm not worried about color matching or anything, but there is an embroidered logo on it. I'm wondering how I can avoid dyeing that part. I was thinking about putting some tape over the logo (and on the reverse side as well), maybe some packing tape that couldn't be penetrated by the dye, but I'm not sure if that would work. I don't have any experience using dye (except for hair dye!) Will this work, or does anyone have a better suggestion? I don't mind if there's a little difference in pigment around the logo, as long as the bleach marks are covered and the logo is untouched. I'd really hate to have to retire this shirt since it's fairly new and in otherwise good condition. Thanks in advance!

Edit: I tried using a Sharpie and it worked quite well. I realized while I was doing so that my shirt was kind of pilly, and some of the bleach only got on the fuzzy outer layer (I don't know how to describe it so I hope you get the drift, lol), so I went over it with a disposable razor as well. It looks a lot better and it's not noticeable at all. Much easier than dyeing it. Thanks to all for the suggestions!