Pass-through authentication is usually Active Directory, in this day and age. What authentication does the web service use? Is it tied to the same AD instance as the users running the robots? If the robot's user has permission to access the web service, you should be able to use pass-through authentication.
If not, the other obvious option is to use the Credentials Manager in Blue Prism and use the built-in functionality to not hard-code credentials into your processes/code.