I first lived entirely on my own at 19. I was in University and I had a dorm room all to myself, courtesy of my high grades.
I did not have a part time job as my course was very hands on, but I worked the year prior and saved like crazy, I received scholarships, I sold some rare video games for extra spending cash and at that time I was receiving $130 a month from my father, apparently family services got a hold of him and tried to get him to pay some of his massive back child support, it didn't last (it stopped about 5 months into that school term), but it was something extra to count on each month. It can be hard to net an income when you are in University, especially if your course load is heavy. I had enough funds so that as long as I wasn't splurging on diapers and baby things every month, I could enjoy myself pretty reasonably and regularly.
It took me a few weeks, about a month at University before I started to indulge, as I needed to work up the nerve, it can be overwhelming when you have space to yourself and ultimate freedom. Once I worked up the nerve, I went pretty hard in my 2nd month at University. I bought two packs of Bambino diapers from a now defunct Canadian AB Diaper distributor, an adult onesie, an adult pacifier and an adult baby bottle and went to town... between studies, homework and nights out with friends of course. I found that if I reserved my AB time for weekends only, sometimes every other weekend if course work was piling up, I was able to stretch my finances as well as my diaper supply. Some weekends, I would even tell my friends on campus that I was heading home for the weekend, so I wouldn't have to worry about them knocking at my door if I was padded up and in baby mode.
Since then, I've had two apartments all to myself and my AB routine is pretty much set in stone; I regress and baby out whenever I can. I am also fortunate enough to have consistent freelance work and I am now a paid scholar as well, so I have much more income now, enough to stock up on diapers and maybe treat myself with a baby outfit or accessories every month.
Now, your living situation may differ from my own. When I was wading into this side of myself deeper, I had a room to myself, not all dormitories are set up that way. You may have to plan out your purchases and really pay attention to your class schedule and your roommate's class schedule in order to figure out when it is best for you to diaper up and baby out. If you manage and plan your time and finances accordingly though, there's no reason why you can't explore your AB side and have some fun. Treat this first year on your own as "baby steps".
Best of luck to you