Directions appear below the screenshots they are referencing.
Open an image and size it to your target size. I use 1200 pixels as my proofing size.
Then create a new action. Go to Window -> Actions, to open the actions palette. In the dropdown (click where the yellow arrow is pointing) create a New Action.
Name it something relevant.
I have chosen to use a text layer for my watermark. You can also use a graphic, such as your logo. Import it using File -> Place. You will now have two layers.
In your Layer palette (View -> Layers) shift-click both layers.
In your top menu, use the alignment icons to bottom align and center align the layers. You can also left or right align the layer if you prefer. Then select just the layer with your watermark and use your arrow keys to give it some margin at the bottom or sides.
Once you have it how you like, flatten the image under the Layers menu.
Stop recording your action by pressing the square Stop icon in the Actions palette.
Open Adobe Bridge, navigate to and select all the images you wish to watermark, go to Tools, go to Photoshop, select Image Processor.
In Resize to Fit, make it the size you did your first image. 1200 pixels in my case. Then check the Run Action box. Select the action you just made. Then Run the action. It will automatically resize and watermark all your photos, and place them in a subdirectory called JEPG within the folder that your working images are in.