No and yes. As far as the official full screen mode, no. All you can see is the image. That's it.
However, what you CAN do is to increase the size of your Bridge's window to fill your screen. The move your metadata window to the left or right side. In the screenshot below I also added the Content Panel so I could go to other images, and removed the other Panels as that's not what you want. When you've got this the way you want, Save the Workspace! I called mine Full Screen and Meta (how's that for a catchy titile???).