Self studying and letters of recommendations
How best to organise your self-study? Pick your 10 favourite PhD programmes and look at their admissions requirements. Those are the courses you need to cover in your self study.

Then read the email you received carefully. Notice that it's not the letter that needs to be special-- it's you. You've already hinted at your drive and motivation to continue studying your subject at graduate level; why else would you devote so much of your (presumably) otherwise free time to studying it outside of classes? This effort may carry some weight with the admissions committee. Think of it as your unique selling point.

Now the tricky part: really making sure that the admissions people understand your USP before they meet you. This is your referees' job, and to help them do it successfully, it's your job to make sure they know and understand you as a student, as a mathematician and as a person. 

In this task, I think communication is the key. Talk to your instructor; tell her your plans for self-study, discuss what topics interest you the most, ask for feedback on your work, chat about relevant literature, where you want to go for your PhD, whether the moon really is made of cheese-- you name it. 

What I'm getting at is that for your letter to stand out from the no doubt tens or hundreds of other generic letters the admissions committee read, you need to come across as a real person with a genuine interest in your subject and the requisite skills and knowledge to back it up. And the only way that will happen is if your referee knows you as such.

(Disclaimer: I've never written or read a reference letter, but I've had some small recent successes in the hunt for a PhD place, largely (I think) due to my reference letters.)