How long do I study on my own before applying to math grad school?
I disagree that this is the right approach. Many grad schools in the US would require you to have a Bachelor's degree in some subject and to make up the courses you missed by not having a Bachelor's degree in math. So your best option is to get started actually completing those courses. I think that unless you have some publications in math with someone who can vouch for your skills even though you don't have the coursework, you're not going to get into a good Master's degree program without the necessary coursework. The further your history is from the required classes, the more work you're going to need to do. Some programs might admit you with the requirement that you take a few semesters of undergrad classes to catch up, but if you need more than a few catch-up courses, you're really looking at a second Bachelor's degree or working on the side through a non-degree-seeking program at your local university.