When bash is called non-interactively, PS1 is unset. However, if it's a login shell, ~/.bash_profile is still sourced. Therefore, testing PS1 tells us if this is a login but non-interactive shell (such as: ssh host 'uptime'). Testing PS1 before setting it preserves that state for later tests if desired.

--- a/.bashrc	Fri Aug 28 17:45:02 2009 +0000
+++ b/.bashrc	Sun Aug 30 06:49:10 2009 +0000
@@ -18,7 +18,7 @@
 #
 # Environment variables
 #
-export PS1='\h:\w\$ '
+[[ "$PS1" ]] && export PS1='\h:\w\$ '
 export PAGER=less
 export EDITOR=vim
 export RUBYLIB=$HOME/Installs/rubygems/lib