We had a bathtub put in, and the contractor set it level. The bottom of the tub is now 1/2 inch above the floor and goes to 0, like a skinny triangle. If we build the floor up, it will be to high for the tile to be even with the entrance to the bathroom. Any suggestions?

At the very least, the top of the tile will need to be a touch higher than the base of the tub at the 1/2" part of the build. Assuming you would use 1/4' cement board on the floor, you can count on the total floor height being about a 3/4" build up. If you are on a slab, you could pour some leveler, and in either case, the transition at the door can be hidden with a marble saddle.

In the case of cement board, tile only cares about flat, not level, so though you could install cement board and then pour leveler on top, that would be up to you. Using cement board to build up a slab is not an option, for that you would need self leveling cement.

Are you absolutely certain the tub is level and you've checked the tub deck on all four sides? It's a rare day a tub I see is level... usually means I reset it :D

Try using a 4' level on the floor and put a 1/2" shim under the low side, does this now show perfect level. Please tell us what the flooring is, is it in fact a slab?