How to gain admission to a math PhD program when as an undergrad, I didn't do research, take pure math classes, or form relationships with professors? I just graduated college in May, and I spent my entire college career convinced that I would never study again. I had a plan for my future, and it involved working- no more school. I had considered grad school, but never very seriously. 

Now, however, I am very much considering a grad or PhD program. Unfortunately, because of my intentions before, I hadn't done much research in college, opting instead for leadership and work experience. I also didn't foster any significant relationships with my professors. I talked to them enough to learn the material and pass the class, but, in my opinion, not enough for a glowing recommendation.

Now, I feel like I wasted something. How can I get into grad school when I am unable to procure stellar recommendation or show that I took classes in pure, theoretical mathematics? (I took more classes that concerned mathematics applied, like statistics and practical life models and such)

Would it be necessary for me to take more classes? Go back to school? That seems unnecessary, since I already have a bachelor's degree in Math, but I don't know what I can do.
How can I get into grad school when I am unable to procure stellar recommendation or show that I took classes in pure, theoretical mathematics? (I took more classes that concerned mathematics applied, like statistics and practical life models and such)


I think you need to take courses in pure, theoretical mathematics.  You can do so:


As a non-degree seeking student at a reputable university, probably self-funded.    
As a master's student at a reputable university, possibly self-funded.


By a "reputable university," I really mean one with a solid math PhD program or a very strong master's program.

Presumably you want to do this while still keeping gainful employment, so I would start slowly: maybe take one solid course, really try your best, and then reevaluate whether this is what you want to do.  If that goes well, repeat and intensify.  I would plan to spend at least two years doing so.   

Once you start doing well in courses, make a point of talking to the instructors and getting advice from them.  Maybe they will encourage you to apply to the PhD program there, or maybe they will have other good suggestions for what to do next.