You can add custom CSS directly to CBs default template using its overrides feature. See the below for further details.
www.joomlapolis.com/blog/kyle/18711-template-css-overrides-made-easy
For even more customization you can use CB Template Changer and its Template Builder to generate a new template for CB. See the below for details.
www.joomlapolis.com/blog/kyle/18797-template-builder
To load a custom CSS file you'd need to use CB Auto Actions with its Code action and Method set to "CSS (URL)". As for what triggers to use it'd depend on where you wanted it to load. For example if on profile you'd use onAfterUserProfileDisplay. Will be happy to provide additional triggers if you intend to use this method and can provide where you'd like your CSS to load.