I've checked the camera raw preferences and they are both 9.1 so I should be able to see the images but am not able to open them to edit. I've also checked the preferences on Nikon Transfer to see if there as something off there but everything seemed OK. I'm also not able to convert the .NEF files to .dng files so I could edit those. Please help.
Are you getting any error message while opening those images?
Please share the error message with us.
As you have already described that both Photoshop and Bridge are running on camera raw version 9.1 but I would like you to close both the applications and also try installing the latest camera raw and then try to open images.
Camera raw install link:
Please let us know if it helps.