This is possible but it all depends on your present room set up. You can move doors, but it is more costly to move plumbing. I did a guess and made you a mock up using your dimensions. Here I have used a 48 x 34 inch shower and added a small but doable closet. Not sure where your windows are etc. Hope this gives you a visual:

http://www.roomle.com/app/editor/8a701c3153561e970153615e67b65374

First time tried this, but made a rough layout of my bedroom. Click the above link

So what are the dimensions of your bathroom and is it just tacked on the room? If so then it is not part of the 20 x 14 ....???? Are your closets part of the 20 x 14? I am guessing they must be. Let me know before I re do the mock up.

Oh and in your bathroom, where is the toilet and where is the sink? And is there a window in the bathroom????