iOS does not permit another app to access iBooks data. So I would suggest storing the PDFs directly in AirMount app, so you can access them from your Mac.
Yes, AirMount integrates with the native iOS Photos app for accessing photos and videos directly from the Mac’s Finder. It supports all file types through a built-in “Drive” where you can store PDFs, documents, email attachments and documents from the Mac that you want to carry in your phone, without sending anything to the cloud. From the Drive, you can preview those PDFs and files, and share via other apps. I love that I can just drag and drop stuff between my devices and it feels very natural, personal and quick.
I have been working on this area for 2 years now and created AirMount https://www.airmountapp.com. You don’t need the cloud, internet, Bluetooth or USB. Today it works between iOS and Mac, and now we are building it out for Windows and Android. I dream of the day when sharing files with any nearby device will just work like AirMount does today, irrespective of their OS. The industry needs to collaborate to make open standards, but in the meantime I intend to push the limits of what is possible already.