To get admitted to a graduate program in math, although work experience may suggest greater maturity, etc., the issues will be letters of recommendation and documentable standard-material background (whether in conventional courses or somehow-verifiable self-study...), and possibly a GRE subject test score if only to show that one is aware that the thing exists and is widely believed to be relevant (even while many, including myself, do not consider it a good predictor of anything much beyond multiple-choice-test-taking abilities).
Unless you've self-studied into a quite unusual state of expertise, you'll most likely not have much success in getting an idea of what contemporary research in mathematics is about, and it might be awkward to attempt a conversation with faculty about their current work. Perhaps such a thing would be feasible in other fields (I have no idea...) it is not typical in mathematics. That is, people going to grad school usually have only a general idea of the direction of their interests, even with a solid coursework background. In particular, funding for graduate work is rarely dependent upon connecting with any particular faculty more than tentatively. (Again, this is evidently unlike other fields.)
Helpful letters of recommendations would be from professional mathematicians actively involved in research, acquainted with graduate programs in mathematics, who can speak from direct personal experience both about what such programs will demand of you, and about your qualifications to meet those challenges in terms of prior preparation and in terms of interest.
Probably the way to put yourself in a position to have such letter writers is to take upper-division or beginning-graduate courses at a solid university, as a "non-degree student", do well, and thereby be able to ask the instructor for such letters. It's not the credits themselves, but the information and the certification by faculty (beyond "getting a good grade"). That is, you'll want people to attest to your future potential, beyond accomplishments to date, in the sense that (hopefully) "you've only just begun", rather than having peaked-out.
If you are an outstanding multiple-choice test-taker, getting a stellar score on the math subject test GRE will catch the eye of many! :)
Other routes for certifying that your self-study has made progress are difficult. E.g., certificates from on-line courses are not worth much, and, most often, those courses are too elementary to be relevant to graduate study in mathematics.
If you are not geographically flexible, going to the nearby universities mathematics departments and asking "what it would take" for admission, _with_funding_ (don't go without funding), and try to do it. The whole process might take long enough that it'd be wise to keep the job you have, even if you don't like it, to support yourself (and others?) through the preliminary stages of gaining entry into a graduate mathematics program.