Yes, of course, there are many places you could publish research at your stage. For one thing, many undergrad journals will accept papers from recent graduates as long as the research was started when they were an undergraduate. Another option would be to team up with some other undergraduate and write a paper together.
There is also the Graduate Journal of Mathematics (full disclosure: I am an editor there). You don't need to be a grad student to get published there. The website explicitly states that a good bachelor's thesis project could be acceptable. And, of course, if you do work at the level of a professional journal like the Journal of Pure and Applied Algebra, you could publish there. They have published papers by undergraduates and recent graduates of Reed College (students of Kyle Ormsby), for example.
All that said, I agree with Dave Renfro that a better way to strengthen your application for a PhD program is to demonstrate success in graduate level courses. You could do a post-bac program like Smith's. You could audit grad level courses at a local university (and try to get a letter of recommendation from the professor who can speak to your potential). You could apply to master's programs instead of PhD programs. As Dave said, the upshot of showing depth via coursework is that it's more likely to succeed than showing depth via research (after all, grad school is meant to teach you how to do research), and also the coursework you do will help you pass your qualifying exams when you do eventually get into a PhD program.
