Re: bathroom flooring issues
Can't really tell from the pictures if the new bathroom floor is tile or vinyl. If it's tile, remove the bottom course of sanitary tile and custom cut a piece of the floor tile to fill the gap and act as the baseboard. You'll want to line up the grout lines on the floor with that of the baseboard for the best aesthetics.
If the floor is vinyl, the YukYuk's suggestion is probably the better route.
I suffer from CDO ... Its like OCD, but in alphabetical order, LIKE IT SHOULD BE!!!