Stumbled over an old entry on the SANS ISC blog today that explains how to set up bash for remote logging of it's command history (it's a compile-time switch): SANS: Improving Bash Forensics Capabilities (cache)
The post also has some more information on the various environment variables that control bash history options.
Since the version 4.1, Bash supports Syslog natively but in most distribution, it is not enabled. To use this feature, you need to recompile your shell. [..] You just have to define "SYSLOG_HISTORY" in config-top.h
The post also has some more information on the various environment variables that control bash history options.