Complete Tile Collection carries two lines that might meet your requirements...

Look at Pratt & Larson and Fireclay tile. I have recent experience with both and selected them partly because of the many trim options. They have many whites, but you might have to pick your trim pieces from a diagram because they're custom.

Those tiles look amazing. Elunia" Have you ever used them yourself?

Walker Zanger 6th Avenue has a white gloss but not sure how white it is as I was focused on finding a blue. This is Walker Zanger's more "affordable", "quick ship" line from what I've been told and more affordable than most Pratt & Larson for example which I also looked at. (I'm using the WZ pale sky gloss in a 6" hex for a bathroom project that has yet to begin.) It has lovely mouldings and does have bullnose pieces. However, the mouldings are expensive, even in this more "affordable" line. Luckily I don't need any of the molding pieces.

https://www.walkerzanger.com/collections/products.php?view=mat&mat=6th+Avenue&coll=6th+Avenue

You could also consider Sonoma Tilemakers Stellar Quickship Collection which is also "affordable". In the Steller Quickship line, there is a "Blanco" gloss which is white (can't remember how white it is though) and there are lovely mouldings and bullnose to choose from. My mom used the 4x8 bossy gray from this line for her bathroom backsplash, including bullnose pieces.

https://sonomatilemakers.com/stellar-quickship/

If you have more money to spend, Sonoma Tilemakers' regular Stellar line (not the quickship) has "Pure white" in addition to "Blanco" and even more liners and mouldings to choose from.

https://sonomatilemakers.com/stellar/

To give you an idea of pricing, for me, the WZ 5th avenue 6" hex is approx $24/sq ft (w/o contractor discount) or $19.50/sq ft w/discount. The WZ 3x6 bullnose is approx $9.50 per piece (w/o discount) and base moulding is approx $21 per 4x8.5" piece (w/o discount).

Sonoma Stellar Quickship (for the bossy gray color at least) was approx $18/sq ft for the 4x8's (w/o contractor discount or $14.50 w/discount) and $25.50/sq ft for a non-quickship glaze (w/o contractor discount).

I also looked specifically at tile lines with architectural trim pieces including Vermeere, McIntones, Pratt & Larson, Fireclay, etc. for a bathroom renovation we are currently undergoing. Just like Skippack Tile & Stone suggested, I either looked at the tiles in person or ordered samples - they all have different ”personalities!” I ended up choosing Heritage Tile Subway Ceramics because of the extended p-cap/chair rail plus the tile allowed the tightest grout lines. We have an 1888 Victorian and while we were not looking to recreate a period bathroom, we did want to reference the age of the house. And, as adawn5 noted, all these mouldings are priced by the piece and it adds up quickly!

These are all great suggestions. Some I've already looked at and some I'm going to look up. I did like the Sonoma Tile Pure but was advised at the tile store that the tile could fail in a wet environment. Someone also posted here about Sonoma Tiles that were sealed failing in the shower so I'm ruling them out...I did get a sample of the Heritage Tile and it's beautiful. The white color is a little warm but it might work. I'll look at their trims too. Haven't looked at Fireclay yet. That's next. Didn't really want to get into custom tiles but might have to. The 5th ave. from WZ is pretty. Saw it at Virginia Tile, a local tile store, but the white color wasn't working when I brought home a sample.