I have heard that enamel can thicken/grow back but what can I do to thicken it so that the dentin does not show through?

Prior to my Zoom treatment my dentist said I may not see results because my enamel was thin and the color/gray was due to the dentin or root color showing through... it would only work if the bleach would penetrate through to the dentin. No success and my front teeth are the issue with uneven discoloration. What are my options? I will try just about anything before getting veneers. I have heard that enamel can thicken/grow back but how can I inhibit it?