We are unclear on the specifics of the VirtueMart bridge. From the user manual we could not infer the recommended setup (is there any other documentation?)

Is it possible to install one VirtueMart into the core and manage all products within this instance? We would like in this scenario that the slavesonly show certain categories using their design and for checkout the shopper would end up always in the core instance.

The VirtueMart bridge is used when you want to propose billable website creation from the front-end.
In this case, we provide a ready to use solution that consist to use VirtueMart to process the ordering of a website creation and also to process its payment.

This bridge is NOT designed to provide a "shared" virtuemart between websites.

We are currently working on a JMS 1.2.x that will give the possibility to share the users between website and also have the possibility to share VirtueMart between websites.
This will give you the opportunity to share the same product catalog between websites.

We hope to have this new JMS 1.2.x available in june or july.