It's almost impossible to answer a question like this without pictures.....of the tile, the wall color, other fixtures in the bathroom, the style you're going for, etc. In the absence of any other information I would say the wall color is often a good choice for grout color, as it ties those elements together --- but again that depends upon both colors and how they look in the actual room. You will get a lot of well thought out and helpful replies from others here far more experienced than I if you post pictures.

The red mosaic tile sounds interesting and I'd love to see it.

The tile people I dealt with, when I was redoing my home, had an in-house decorator, and she allowed me to choose what I wished but if I ever made a decision she did not agree with, she told me and gave me the rationale behind her disagreement. Believe it or not, she could always prove to me why she said that and I would always, albeit sometimes too late, see her point.

If your tile people have an in-house decorator, that is a good service, so ask there. They know your house, your tile and have the experience with each kind of tile and the granite, etc. Had I listened to her, I would not be stuck with this absolute black granite!!! which she advised against. Hindsight.

Do you want pattern , ie, contrasting grout, or do you want it to read mostly as a red textured surface? Fresh or more earthy?

Here is the mosaic countertop/shower floor/niche tile next to the wall tile. The wall tile is shiny white. There won't be much paint on the walls, but the paint will probably be white.

The floor tile is a large-format "linen-look" beige porcelain tile.

The vanity wood is white. So is the toilet and sink.

The fixtures are polished nickel.

The door and window trim are a reddish-brown wood.

Did you see a display board for the red tile at the tile shop? Usually the display boards are set up with a grout color that enhances/complements the tile, so that would be a good place to start.

I would use a warm brown. But I would use a lighter tan for the bigger white tiles.

Just remember when you look at grout in its tube or pan (whatever is being displayed), it is going to dry much lighter and it darkens as it ages.

I agree with kswl...warm brown. Love the red tile!

Have you considered adding a bit of sparkle in there? Mapei has some interesting 6% gold or silver grouts (see link)-- perhaps MG750

if thats too much maybe find a dark undertone in the tile that blends in with the overall color. Your tile shop should be able to lend you the grout color bars. Take them home and look at the tile in your space under different lighting conditions.

Here is a link that might be useful: mapei

If it were me, I would try to match the grout with the darker red in the tile so it's not obvious. That way it won't compete with your floor and wall grout.