In theory, Responsive is more bottom-up than what you describe.
- First, you make sure your site/app works in the most barebones browser, with minimal support of CSS and JS.
- Then you build up from there, adding "icing" with greater browser capabilities and window size.
It also about not just using the breakpoints, but also making some things scale sensible in size, width, height, as the window is resized.
In practice, just by using Bootstrap, you're gaining the above capabilities. You shouldn't have to do too much more other than make some decisions in the media queries for certain components to show or hide, like you describe.
- Include the responsive stylesheet
- Use the fluid versions of containers and rows, like:
Here's the relevant Bootstrap docs: