Implement toggle switch for theme options in settings API

There are several ways to implement an options page. You can implement a quick and easy options page via Advanced Custom Fields Pro (find out more here: https://www.advancedcustomfields.com/resources/options-page/)

To do things the WordPress way(without the help of plugins), you will want to follow this guide here: https://developer.wordpress.org/plugins/settings/custom-settings-page/

Once implemented, you should be able to save options via a custom options page. To get the value out, you can use get_option("YOUR_OPTION_KEY");.

In regards to styling, you are correct – WordPress does have their own CSS to support administration pages. I would recommend leveraging those instead of using Bootstrap.