Someone is responsible for maintaining/patching your servers. Either you are, or you are paying someone to do it.
If you are paying a company to do it, send 'em an email. If you are responsible, look into what it takes to install a bash upgrade. I was able to patch my own Ubuntu VMs in about shell 3 commands manually through SSH (yay apt-get). Took all of 10 mins reading up on documentation, logging in, hitting yes to prompts...
In all seriousness, the patching process shouldn't be too much more involved than patching your desktop OS for a small shop not worried about 100s of servers, load balancers/failover mechanisms, SLAs, etc...