From a financial standpoint, how much more can I expect to earn after my degree? While certainly there is value to learning something you are passionate about, one might also have to consider the finnacial responsibilities after college. Thankfully for me, what I am passionate about is also what I can expect to make a decent career out of. 

I am entering college as a mechanical engineering student, however I feel like I would very much like to pursue a double major, the second degree being in math. While what drives me to this is my interest and passion in the subject (Ive always been a fan of numbers), I can't help but pause to consider if the extra time and money spent is practical. In short, how much more can I reasonably expect to make with a bachelor's degree in math and in mechanical engineering, upon graduation?
Pursue the dual major because it interests you and this is your opportunity to do  it, not because you expect a higher salary, because the higher salary probably won't happen.

I spent a long career in industry in engineering before coming out of retirement to teach a few years ago.  In my experience, hiring managers generally don't care that someone was a dual major.  Part of this may be a reflection of the fact that managers tend to hire people who "look like them".  Not very many managers were dual majors, so they don't value it.  But there's a practicality to it as well:  If they're hiring you to be an engineer, it's probably because you are an engineer, not because you're also a mathematician.

What hiring managers do value is the master's degree.  Again, this may be in part because so many hiring managers have master's degrees (which many of them may have earned part-time while working).  Hiring managers tend to have master's degrees, so they like to hire people with master's degrees, and they will pay more to get them.

If your concern is best financial return on any additional effort beyond what it takes to get a bachelor's degree, I recommend going for the master's over the dual major.  Many universities have programs that allow students to go straight through to their master's, double-counting some of their credits and earning both degrees with just one more year of coursework only, no thesis required.  For example, here at University of Michigan in computer science, where I teach, it's  called SUGS (Sequential Undergraduate/Graduate Studies); to be admitted to the program you need to be a junior or a senior with a 3.6 GPA.  Your school probably has a similar program.

If your objective is a career in industry and you're concerned about "bang for the buck", the master's is the way to go.