Hi Tantavi, for what it's worth, I say go for the Fulbright.
To me, it seems like you're debating between what you want to do and what you think-you're-supposed-to-do. In my very limited wisdom, the think-you're-supposed-to-do path is safe. It feels Responsible and Adult. The supposed-to-path makes a lot of sense in a lot of situations, but not this one.
In this situation you win on all fronts if you take the Fulbright.
You're worried about your job prospects - Take the Fulbright. For every job you apply to, there will be stacks on stacks of resumes from people who, "skill-wise", are just like you. If you rock, which I bet you do, and you stand out, which a Fulbright will help with, you get the interview. If you forsook the Fulbright, one year from now you will stand out as much as the thousands of other math/comp.sci people a year into an entry-level job. Point: Fulbright.
You're worried about money - Take the Fulbright. You're playing the long game. The difference between coming out of college broke now, or a year from now is negligible. Spend a year kicking ass and taking names, developing soft skills and honing an interesting interview-narrative. It will pay off. Credentialism is also important (unfortunate or not). This is a big, fat, stamp of approval hiring managers will use when looking at your applications. Point: Fulbright
You're worried the Fulbright won't give you "skills" - Program in Bulgaria! Choose a project, knock it out, and add it to your CV. Realize that you will develop communication skills, soft skills, and self-reliance abroad. Recognize that those skills have worth. As an aside, have a look at Sarah Kendzior's tweets about the our modern idea of a "skills gap" here and here. She can be bombastic, but what she writes there is at the heart of my fears of incompetence, it might ring true for you as well.
TL;DR: Your Fulbright is a one-year investment in your future - you are paid, housed, and your loans are deferred. It doesn't get more low-risk than that! In the worst case scenario, assuming you don't hate the experience, it will leave you in the same position you are in now (few "skills [...] and prospects"), but with a wonderful year abroad that you will always have memories of. In reality it will provide you with tangible benefits, detailed above.
Best,
Isaac