As an electrical engineer, should I study pure mathematics in my spare time or do a second bachelor degree?
From your question, I assume that you are NOT interested in taking a degree in mathematics because you need to prove to somebody that you have a qualification. What follows is based on that assumption.

Learning 'pure math' is not the same thing as learning a language: pure mathematics is a myriad of languages. A bachelor's degree course in pure mathematics traditionally covers, shallowly, a very wide range of topics, most of which the students will never use again, even if they pursue careers as full-time professional mathematicians. 

I strongly suggest to you that if you need a better understanding of some aspect of pure mathematics for some particular purpose, then you should study just that aspect of pure mathematics. You may need to rewind a bit to find a starting point that you do understand. And you may need to broaden out your reading as you go along. 

If you have no particular purpose in mind, then just pick something that you are interested in. Do not expect to understand everything immediately. Do not be afraid to pick up non-academic 'popular science' type books. There are so many entry points that I am sure you will be able to find one that suits you.