I am in my last 5 classes of my MA in Bible. The program does not have advisors. We have a program director who is the dean pro tempore, a professor of record for every class and a social liaison to other universities. This is a very small school (only 576 MA students and 29 PhDs). I want to start writing for publication so I went to the program director and he said my writing was ideal for publication but he said I would need to outsource and he was not willing to do that at the time and he said I would need to find someone with comparable academic interest. Then I went to my current professor in a class on Johannine Theology. He said I needed to find an advisor but I do not know how to go about doing that. So how can I do this? What do I need to do? I think I want to go as an independent researcher if that is possible.
If you don't need to submit your writings to the school for graduation then you can do as you please and submit it to an appropriate journal.
The Dean's advice is, perhaps, nothing more than a warning that you aren't quite ready for "prime time" yet and that your work needs refinement. That may be true or not, but it isn't a block on independent work. (Alternatively, and I hope not, they are suggesting your work is too controversial to have it associated with the school. In that case, take warning and wait until graduation to proceed.)
The best way to contact outside help is through a current professor; a recommendation to an external colleague. But if that isn't possible it raises a flag. If they are too isolated/insulated that they don't communicate with others then I wonder about their competence as researchers. That is possible in small schools, but not desirable.
If you can't contact people that way, then the other option is to find authors of papers in a related area and email them with a request to review a paper and give you advice. Make the email short, indicating you have read their work and saying a few words about your own, but waiting until they agree to send the paper.
You will, of course, get feedback, even if cursory, from any reputable journal that you submit your work to. It may take a while for review, and more so if it the work seems significant at first glance.
Long term, however, start to develop a circle of contacts and potential collaborators. You can share and refine your work in such a circle as well as use it for new ideas to pursue.