Silicone caulk is about the only way I am aware of. And it will be fairly obvious unfortunately.

If you have or can get an extra one, replace the tile. If not, a dab of silicone.

Tint some thick super glue, overfill the hole, hit it with accelerator from the hobby supply shop, scrape it to flush and polish. It will be more inconspicuous than silicone.

@Joseph Corlett, LLC What kind of "tint" for thick super glue it's just a cream colored tile?

Interested to know what you can tint super glue with.

You can use baking soda as an accelerator.

What about a hole plug?

I've got pictures now of what I'm dealing with. I'm wondering if it would be better to cut out a few random tiles and replace with decorative tile. I just don't think it's going to be possible to fill 4 holes and hide them. There will be a 24" slide bar for the the hand held shower right next to the tile with holes but it won't in any way hide those holes.

Maybe look for an escutcheon plate to cover the holes if your slide bracket will not be that far away.

P McG:

I've tinted super glue with nail polish. Lotsa color selection at the drugstore.

The tile, caulk & grout are all pristine. When was the tile work done? Do you know or can you find out who installed it?

What I'm getting at is that it may not be impossible to find a match & replace that one tile. It looks like a very basic stock tile.