You cannot reference values related to the running context and user in Process Builder criteria, but you can get to them if you set actions to execute if a formula evaluates to true. There, you can click the "System Values" search box to get access to a tree of data sourced from the running context:
While you can add formula references here to the User, their Role, or their Profile, for circumstances like the one you describe the superior solution is usually to create a new Custom Permission and check for that (the "Permission" value tree in the screenshot above).
This allows you to make changes to the behavior administratively, by adding and removing a permission set from a user, rather than by deploying or changing your Process Builder. It's more resilient to changes in your org and desired business process.
A similar process can be used for a Hierarchy Custom Setting.