"sich weiter bilden" is a reflexive, two-part verb in German that means "to continue one's education" or "to go back to school" for something additional.
Because this verb is a two-part verb, "weiter" gets kicked to the end. So you start out with the structure of the sentence as:
Ich bilde ___ --> weiter.
Note that the conjugated form "bilde" is in position 2, the verb position!
Now we need the reflexive form, meine Damen und Herren! The reflexive pronoun for "ich" is "mich," thus we have:
Ich bilde mich weiter.
Subject, verb, reflexive pronoun, 2nd part of the verb.
And this, liebe Leser, leads me to a very important announcement: Ich bilde mich offiziell als Deutschlehrerin weiter! I'm going back to school to become certified to teach German as a Foreign Language!
After 5 years of German instruction and seeing students grow in their German language skills week by week, I've decided to make it official and last week I began the program "DaF Unterrichten" [Teaching German as a Foreign Language] from the Goethe-Institute. It will be 18 months of studying, practical application and exploration and into the 2nd week I can honestly say so far it's a fantastic course.
In line with all the online teaching I do, this course is also an online, distance-learning course. Thankfully we receive hard copies of the materials in the mail--6 books' worth!--so it's not all online reading.
So when you are doing your German homework, dear reader, I'll be doing mine, too! It's so true, that learning is a life-long adventure. Thanks so much for sharing your Germanic adventure with me!