Bates Numbering/Shrink Page

I am not aware of any way to to this in one step, but you can do this in several steps: 

Use preflight to scale down all pages by a certain amount to a new target page size (you would need to experiment to find out what the correct size would be). A while ago, I wrote a tutorial about how to do this with Acrobat DC Pro: http://khkonsulting.com/2017/03/scaling-page-content-in-adobe-acrobat-pro-dc/

In a second step, you would then enlage the page size to e.g. letter again, but this time you can specify where you wan to add the additional space. This is done in the crop dialog, but can also be done via a preflight profile.

And finally, you would add the Bates stamp on the now modified page. 

This is a lot of work, but some of it can be automated. I would recommend you run through these steps once manually to see if the output is worth the effort, and then potentially think about automating the steps.