How much would a new bathroom cost?

Get a couple of contractors in your area to give you a free estimate. You need to have an idea what you want done. There are different prices for hardware (sink, bathtub, commode, faucets), tile, and labor.
When we have anything done to our home, we make sure they are Diamond Certified contractors.
http://www.diamondcertified.org/

I do bathrooms, one after the other.

A friend had a quote for 22 grand, and asked my advice.

I put the same bathroom together for her, for just over ten grand.

This was a total demolish and redesign, including the ceiling and electricals, and minor plumbing changes (flick mixers instead of twin taps)

I made 7 grand for two weeks work.

She was happy, and so was I. It's a tough gig, but I enjoy the results.