Do I need a bachelor's degree to research plants? Publishing my research?

You may do whatever you want to do provided you can pay for it. To get a job as a botanist or have your work accepted by a peer review journal you would need academic credentials of at least a Bachelor's degree if not a Masters or Ph.d.

At least the BS in horticulture or biology. Preferably a postgraduate degree. While you'll learn the biology with the BS, you'll need the more advanced courses in the design and analysis of experiments and such to do proper and acceptable research.

No, but it's hard to do proper, university-level research (the kind that is published in scientific journals) without having earned a bachelor's at the very least and without working at a university that offers you the right facilities. Most people who publish in those journals are scientists with PhDs (or grad students working on doctorates) at universities. They present the right credentials and experience, they've worked in the right types of facilities.