You might be able to get Hex that is a pretty good match. If it's an imperfect match you could do something like a band of different colored hex as a border and then fill in with the nearly matching hex.

How should the new tile be installed? Could a cement board just be placed on the area and then tiled? Or would this be too unstable for a tub to sit on? The floor is fairly even but not perfectly so.

How you do the infill depends on the eventual elevation differences you'll have between the hex you want to keep and whatever subfloor surface you'll have to work off of once whatever flooring you have under the tub is removed.

Cement board is a fine material to tile off of. If you need more depth than that, then you can add plywood under the tub, then cover that with cement board, then tile on the cement board.

When you install the cement board, you first have to bed it in thinset (thinset spread on the subfloor with a 1/4" notched trowel), then you screw or nail it down. The thinset isn't there to bond the cement board to the subfloor. The fasteners do that. The thinset simply fills in any micro-voids between the cement board and the subfloor which eliminates any future vertical deflection between the two materials.

You can use unmodified thinset, about $10 a bag, between teh cement board and the subfloor.

If you want to keep the same size hex under the tub that you have on your floor, as has been mentioned, you can add a border or transition strip on the floor, then install your new hex under the tub.

You can transition with a solid inset piece, or you can add a dot or key (or some other) type of transition:

As has been mentioned, sometimes trying to match things perfectly doesn't look so good when you can't get a perfect match. In that case, you can keep the metarial (marble) and shape (hex) but change the tile size. Add a transition strip, then tile with larger hex, say a 3" marble hex, under the tub.

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Then there is the option of keeping the material ant aproximate tile size, but changing the shape. For example, going to an obong hex:

Or you can shift gears completely.

You have options. Probably too many! lol

If you want to keep things familiar between the new tile and old, try to keep two of the three properties similar; tile size, tile material, tile shape (pattern).

The more you diverge from "matchy-match", the more unique the tub space can become. And do realize there is nothing wrong with that. If the other elements in the bathroom allow it, the tub floor space and the tub alcove can become a design element on its own.

Thank you so much for the great information! I am thinking of using 12" x 12" white marble tile with a 4" black and white greek key border of 1x1 marble tile. There is a marble threshold in the bath, so I thought that might work. The current flooring isn't marble, just the regular hex tile. Any thoughts? The space is small, and I am afraid any attempt at adding more hex tile may look more like a patch job than going in a different direction.

Here are the samples, along with the current floor.