Here's a basic rundown of how schools and funding works. It's possible for an IRR to get a school, but you'll see below why that's tough.
First of all, someone has to fund your orders. Generally there's no incentive for someone you're not attached to cough up money for ADT since it comes out of their pocket. There is Schools ADT, which comes out of a separate pot of money (from N7) that can be used for schools. However, you need approval for the Schools money, which gets submitted by a parent command (for you, I guess that would be the NOSC). You also need to get a seat in a class through CANTRAC (or CETARS...I can never keep the two straight). You'll need the quota for the school before the money request can be sent in.
However... Schools ADT is in short supply right now. I think the latest I saw was PRI 1 personnel only, though Jim may be able to correct me. PRI 1 would be in-rate training for operational units or for a "critical" (my word) need, not some school that sounds cool and you'd just like to do. I don't know what the money situation looks like once the new FY starts.
At the end of the day, just like everyone else has already told you, need to affiliate and become a SELRES. Then at least you'll have a billet and a command to support you, along with entitlement (AT).