What to enter into browser-sync command to run it on Aquia Dev Desktop?
You need to specify the hostname and port (patch.dd:8083) and the path to the CSS files you want to watch. Using the values in your example, you should therefore run:

browser-sync start --proxy "patch.dd:8083" --files "C:\patch\sites\all\themes\bootstrap_subtheme_local\css\style.css"