What you need to do?
1. Open the Connector Service configuration located at C:\Program Files\Bizagi\Bizagi Studio\ConnectorsService\framework
File name is config.properties. Open with a notepad or text editor.
2. Configure the proxy= as the description states. On the image below you will find on the bottom how to configure.
After the proxy has been entered, save the file.
proxy = http://myproxy.com:3030
3. Restart the Connector Service after you have saved and closed the file. REST calls will be routed through the configured proxy.