Is it possible for someone with a BA in mathematics who is not currently a student to get an applied research job? My graduate school applications fell through and I was wondering if there was a job I could do that would keep me improving as a mathematician, or if the best I could hope for is the least invasive mode of sustaining myself while I study/prove in my own time. I don't need much money to live off of, but I do need to support myself. Is it possible to get applied research jobs with a BA? I know there are research opportunities for graduate students and undergraduates. Do these apply to "unattached" peoples? What about part-time or consulting work?
I'll explain my situation. Due to circumstances outside my control I was unable to apply for graduate school. 

In the mean time, I am staying busy until I can apply this fall. Currently:


I am taking programming/CS at my community college. 
I have been studying math, physics, and computer science on my own. I've been on here a decent amount, I do project euler, I have books, there's Coursera/MITOCW. 
I live somewhat close to a very good university (UC Berkeley to be exact). I looked up the professors for ones that are doing research in fields I am interested in, and emailed them. I am current doing some reading with one of them which will probably turn into some research/writing a paper.
I looked at the classes I was interested in at the university. I emailed the professors asking if I could audit them. They all unequivocally said "yes", some even offered to grade my tests or said that homework was peer graded.
I have been tutoring a lot to make money (with a BA you could easily charge $30-40 an hour). If you really want to, you can get enough students to live very modestly while still pursuing your interests.
I know a friend who works doing data science. He might be able to get me an internship at his work. 
The same friend might want to design some programs together.
Once I get a little better at programming, I was thinking about doing some freelance software/website/etc. development. I'm sure I could do projects here and there.


So do NOT feel hopeless. Honestly I feel like my passion for math and science has never been higher, and I feel very positive. There are TONS of things you can do. Please ask me if you want to talk more. :)