The last two times I've had pink eye, I've used regular neosporin found at the drug store. I use a q-tip to apply it at the corners of my eye and on the lids like you would eyeliner. Do this once in the morning and before you go to bed. This has cleared it up very quickly.
Neosporin contains antibiotic ingredients that will take care of the bacterial pink eye.
Warning: Do be sure you aren't allergic to neoporin. Apply a small amount to your inner arm for a couple of hours. If no redness shows up, you should be good to go. My husband is allergic to it and it causes severe redness and swelling on his skin.