Pretty sure @Israel Gonzalez is correct and you can't run a search on search access (owners and such, yes, but not a full list of who has access). What I've done in the past is to assign myself that role then go to the list of saved searches and export them. Bump that up against all public ones via vlookup (you should be able to get what's public via saved search) and voila, you have the ones assigned to that role. Added benefit or drawback, depending on your POV, of this method is that it also catches all searches the person has access to that have been assigned directly to them as a user or via department, class, etc., not just those they have because of their specific role.