Summary of need to know information:
- Linux Mint 13 has been fully patched: just install level 3 updates from Update Manager to get bash update 4.2-2ubuntu2.6 (changelog).
This fixes all reported vulnerabilities (CVE 2014-6271, CVE-2014-7169, CVE-2014-7186, CVE-2014-7187, CVE-2014-6277 and CVE-2014-6278). - Linux Mint 17 has been fully patched: just install level 3 updates from Update Manager to get bash update 4.3-7ubuntu1.5 (changelog).
This fixes all reported vulnerabilities (CVE 2014-6271, CVE-2014-7169, CVE-2014-7186, CVE-2014-7187, CVE-2014-6277 and CVE-2014-6278). - Other versions of Linux Mint are obsolete and will not receive security updates. Either patch bash manually, or install Linux Mint 13 or 17. More information here.
- LMDE is not yet patched, but you can get a patched version of bash from Debian sid. See this post for details. You will find a separate discussion about the LMDE issue here.
Update 30-Sept-2014: User monsta reports: "bash 4.3-9.2 is in LMDE now, the security hole is patched there."
In other words, as home users not running any server software that is reachable from the Internet, this bash vulnerability doesn't immediately affect you.