If I only had Photoshop and Bridge, then I'd select the thumbnails of the set of images to process, then:
1) for full-sized exports, I'd open them in ACR and use the Save button, or
2) for reszing and other simple things I'd use Bridge / Tools / Photoshop / Image Processor, or
3) for more compliated things I'd create a script in Photoshop and run that on them, which can be done either from Bridge or Photoshop.
However, I haven't done things that way for years, now, since Lightroom came out. I tend to process almost all my images with Lightroom, only using LR / Edit in Photoshop for finishing touches on specific ones.