I know our minds tend to think the worst! But, thankfully, most cases of post-menopausal spotting or bleeding are nothing serious. Oftentimes, it's just some sporadic ovarian activity that can trigger a bleed. The ovaries never shut down; they continue producing hormones our whole lives to keep us healthy. But other "benign" conditions can also cause spotting such as thin, atrophied vaginal or urogenital tissues.
Hopefully, you will fall into the majority where it's nothing serious! Please let us know what you find out.