Is the broken bit sticking out of the hole at all? What does the bit look like? If it is fluted(spiral shape) you might be able to use a needle nose pliers to pull it out. Once you break a drill bit off they usually are stuck where they areif you can't get them with a pliers. Can you drill another hole somewhere and just caulk the one with the broken bit?
Thanks for your interest but, no you can't see it so I think, as you say I'll have to move either up or down. It will be covered with the shower door frame. I gave up and ordered a diamond bit from CA so hopefully it will work.