I think a strong possibility is the Agave Snout Weevil, which attacks Agave and related plants, including some Yuccas.
Here's a link to some info in it:
http://ag.arizona.edu/pubs/garden/az1399.pdf
The evil weevil bores into the base of the plant and lays eggs.
The eggs hatch and the resulting...
Do you know what kind of bush it is?
I could be more helpful if I knew.
If you can post a picture that would be great.
If it's not a serious disease issue you may be able to just prune off the dead wood and let the bush grow back out.
If it is a disease you will want to remove the whole thing it...
I highly recommend attending a class on the subject before you start.
My wife and I attended a free class at our Home Depot store and I was VERY glad I did.
We did it ourselves (floating laminate), it was our first time, and we did a fantastic job!
The main thing with the layout is to avoid...