Someone stole from my wallet, how do i find out who it is?

A couple weeks ago i brought 20$ to school. I had left it in my wallet,in my purse, by accident. During one of my classes a guy kept taking it out of my purse to mess with me. But i saw him put it back before he left, i even checked it. I was gonna take it out of my purse when i got home but it was gone. I confronted the guy about it but he swore he didn't take it, plus he was a friend of mine and i saw him put it back. I just decided to forget about it, assumeing i'd probably lost it. But about a week or two later i brought $5 to school to buy lunch. I let a couple of my friends take $2 to buy me a drink. I was left with $3 in my wallet. And once again when i got home i tried to get it but it was gone. I started to get suspicious. So i thought about it. I knew the only time i didn't have my purse with me was while i was in P.E because i would leave it on the bench in the lockerroom. So now i knew that if i ever brought money ,in my purse, to school i would have to put it in my locker.Not on the bench. So, another couple weeks later i brought some money to school only for a school event. I spent a few bucks but still had $20 left in my wallet. I went to the lockerroom but forgot about putting my purse in my locker. Bad mistake. I checked my wallet on the ride home and my money was gone. I was really upset this time. The total of money the person got from me was $43. That's quite alot for someone my age and some of the money i worked hard to earn. I thought about it more and found this out. Whoever was doing it had been checking my purse almost everyday. It was a girl mostlikely in my gym period. The person couldn't have been sneaking it during gym class because you cant ask to got to the restroom that much.( The only way to get in the lockerroom during gym is to ask to use the restroom.) So, they were either checking my purse before i came in to get ready for my next class (Which i dont think there's enough time to do.), or they were checking it after i had already left the lockerroom and headed for gym (more likely). I don't care about the money as much as i care about knowing who took it. Alot of people know and like me in that class, i have friends in that class who stay in the lockerroom later than me, and i am known for haveing a purse (few people do yet). So who would do that to me? What if it was a friend? How do i catch them?