Hi, Barbara. Mayonaisse or petroleum jelly do a nice job of removing white water rings from wood furniture but not for this problem.
There are a lot of different countertop materials. What do you have? I would be kind of surprised if the bleach had any effect on laminate like WilsonArt or Formica. I don't know enough about solid surface materials like Korstone or Corian to comment. Barb, your best choice of an expert on this is probably the people that sold or installed your countertop. Give them a call.