This is not a problem most likely. If the wire is of sufficient size for the amperage of the floor pads and this is the only thing on the branch circuit (most likely it is), then all you need to do is replace the breaker with a single pole one of appropriate rating (yes, you can probably just use one side of the double pole, but you may wish a small rated breaker anyhow). Take the other wire and connect it to the neutral bus. Please remark both ends of the wire you move to neutral WHITE.

The sticking point is going to be the sizing on the wire feeding the existing controller. Depending on the size and configuration, radiant floor heating can draw a pretty large current. The wire needs to be large enough to handle that current and not overheat. This is a safety concern, so you need to be sure you are using the right wire and the right breaker.

Typically the installation instructions for a radiant floor will say "requires a x amp dedicated circuit". Even if it doesn't, I would not want to tie a radiant floor into a regular bathroom circuit. The first time someone tried to blowdry their hair while the floor was on, it would likely trip the breaker.

I already warned him to check the rating. However, these things even for the largest sized rooms rarely go over 2000 watts. The ones typically sold for bathroom are down around 300.