Turns out that the instructions in the AWS bulletin don't apply to Elastic Beanstalk deployed servers. After some searching, we found the answer.
First determine which AMI you are running:
And then install one of the following patches.
For Amazon Linux 2013.09
sudo yum install -y http://packages.us-east-1.amazonaws.com/2013.09/updates/556c442ced2f/x86_64/Packages/bash-4.1.2-15.18.20.amzn1.x86_64.rpm
For Amazon Linux 2014.03
sudo yum install -y http://packages.us-east-1.amazonaws.com/2014.03/updates/e10f5b547e18/x86_64/Packages/bash-4.1.2-15.19.amzn1.x86_64.rpm
This was found in the following post.
If you are just updating a EC2 box NOT deployed with EB, then simply running the following should work:
"Yum package manager"
sudo yum clean all sudo yum update bash
"apt package manager"
sudo apt-get update sudo apt-get install bash