I don't know where you are, but at least in the US, research experience is not expected before enrolling in a PhD program. It is also not expected that you have take graduate-level classes, unless you are trying to get into a top program. However, it is true that admissions committees want to see that you are sufficiently motivated and committed.
My suggestion is that you apply to several masters programs and maybe a few PhD programs you are interested in. You may or may not get into the PhD programs, but it's easier to get into a master's program first. Having done a master's in math should be sufficient evidence that you're serious about doing a PhD (if indeed you still are), and this will make it easier to get into a better PhD program.
As you will need letters of recommendation anyway, I also suggest you contact some of your math professors from undergrad and let them know of your intentions. Then you can also ask about letters of recommendation and see if they have any suggestions for which kind of schools you should apply to. (By looking at your CV and transcripts, they should have a reasonable sense at what kind of schools you have a good shot at.)
By the way, as a bit of encouragment, many excellent mathematicians have started off in other careers, and your situation of wanting to do a math PhD after trying something else is not uncommon.