You can always navigate in Bridge with the mouse, but it's often more efficient to do so from the keyboard.
In the Folders panel, the up and down arrow keys move up and down one folder at a time. Adding the Command key moves up one level in the hierarchy. The right arrow key expands folders containing subfolders; the left arrow key collapses them.
In the Metadata panel, Tab advances to the next editable field, Shift-Tab to the previous one, and Enter commits an entry. In the Keywords panel, the up and down arrows move up and down the keywords list.
In the main window, the up, down, left, and right arrows move the selection to the next thumbnail in their respective directions. Adding Shift extends the selection to include the next thumbnail in that direction. (You can't, however, make discontiguous selections from the keyboardyou have to Command-click the thumbnails to add noncontiguous images to the selection.) Home selects the first thumbnail, and End selects the last one. Command-A selects all thumbnails, and Command-D deselects all thumbnails. Command-Option-L selects all labeled images, while Command-Option-Shift-L selects all unlabeled images. Last but not least, Command-Shift-I inverts the selection, deselecting the selected images and selecting the formerly unselected ones.