I would prefer writing my own CSS to using any other framework. But there are things you can learn from a framework.
1. Best practices: When you read a frameworks code and question why they have made some choice over others? you will understand what's the best way to write the code.
2. Modularity: This is very much important which saves time and effort in debugging. For example, instead of writing all the styles in a single file style.css, you can split into various files and then combine it later. SASS or any other CSS pre-processor is best for achieving modularity. When you read the code in the repo you will get an idea of how to split a code? and more importantly when to split a code?
3. Bad Practices: No piece of software that has been written is perfect. Each one has it's own pros and cons. Talking about CSS frameworks would you recommend !important for overriding properties? obviously, it's a bad practice. But you can find this in frameworks because they built the framework, not for a specific site but generally for all which will cause some tradeoffs. So learn and verify what they don't do right.
4. Responsive Design: Now to your exact question, not by learning bootstrap classes but by learning how to read the code behind those classes will make you an expert in responsive design. You can use media queries at any width but why do they use at specific points? Is that holds true for all the cases? Bootstrap has five different breakpoints, MDL has only 3 and Bulma also has 5 breakpoints. study how and why do they do that?
So finally I would say learn bootstrap or any other framework but understand how to do it or try to do that same thing with CSS first by yourself.
CSS3 has improved a lot bringing even CSS variables. Give it a try and you will never regret learning it.