In Adobe Bridge, you can do the batch image processing by going to Tools -> Photoshop -> Image Processor... (You need Photoshop installed).
Then select the location to save and resize the photos as you wish. It won't give you the option to select the file size, but you can apply the right Quality, so with trial and error you will know which Quality you need to set to expect the specific image size.
Or if you've access to the terminal you can do:
sips -Z 1024 *.jpg (make the backup first, if you want to preserve images with their larger size).
Also there is easy way of resizing the images using Preview. Select a group of images and open them all with the Preview App. Once they are opened in Preview, Select All, either by hitting ⌘+A (Command+A) or by clicking the Edit menu and select that option. Then go to Tools -> Adjust Size, enter a value for the new width and height, then hit OK. Go to File and click Save All or to save a NEW resized version, choose Export Selected Images or just Save As.