Note: while you are correct that this aspect of the Sixth Amendment does apply to the states, not every aspect of the Bill of Rights does. (Honestly, who here knew that?)
Nonetheless, the vast majority of the Bill of Rights *does* apply to the states due to the Due Process clause in the 14th amendment.
The Wikipedia article below has a good summary of which parts of the Bill of Rights have been incorporated into the states and which ones haven’t.
http://en.wikipedia.org/wiki/Incorporation_of_the_Bill_of_Rights
The Wolf