It sounds like you have a very well-defined design vision in mind, which is a good thing.

But IMO, there's no more durable floor for a bathroom than tile - stone, porcelain or ceramic. One of the prettiest floors I've ever seen that might work well in a cottage bath is a diamond-checkerboard in two soft-contrast colors. By soft contrast, I mean not black and white, but two colors that are close in tone depth, or even the same color but one in matte, the other gloss. I think the prettiest one I ever saw was done in travertine and grey limestone. Just enough contrast for visual interest, but not enough to be distracting.

A warm octagon-shaped terra-cotta style tile could also be lovely and cottagey. Or a cobblestone look.

I would not do wood in a bathroom because you're just daring something to leak! And wood-look tile -- well, they just seem fake.

It sounds beautiful! I have a similar color scheme and aesthetic, and am debating among basketweave, penny round, and hexagon floor tiles, all in white.

Check out Arizona tile's MC series Crema Marfil in a country finish. It is a marble on a semi-vitreous ceramic body. But you have to see and feel it to appreciate it - the web is useless for that. The country finish feels like marble that water has worn down for hundreds of years (at least, that's what it feels like to me) with veins worn deeper, etc. The reason I think it might work for your cottage look is it has a warm, time-worn, natural look (and small amounts of stone in a cottage add another texture). Any tile store with Arizona or Sante Fe tile displays should have it. (If you couldn't already tell, I'm planning on using it when I get to the flooring point of my upstairs bath!)

One of the bathroom idea books around features a picture of a freestanding tub set on a floor of 1x1" tiles. Glazed color ceramic, I think, although honed stone would be great too. The rest of the room is simple, the color of the tub or similar, I think, and it's exquisite. The tiny calm pattern of the tile sets off the tub wonderfully, and it's very much not the typical same-old while also not being gimmicky.

I think white hexagon tiles would go well with your look too. Or basketweave tiles.

Another nice cottagey look is to use 12x12 or 12x24 and lay them in an offset or running bond (not sure about my terms, but I mean like subway tile).

I saw a home in Cottage Living magazine that had painted wide plank floors in the bath. It looked really nice! The issue was in the past couple of months if you can find it.

I think the hex or basketweave would also work.