How can I disable Bash sessions in OS X El Capitan

This behavior is defined in /etc/bashrc_Apple_Terminal. It contains documentation comments describing what it does and how to customize it.

You can disable the per-terminal-session command history feature by setting SHELL_SESSION_HISTORY=0 in your ~/.bashrc script, as described here:

You may disable this behavior and share a single history by setting SHELL_SESSION_HISTORY to 0. There are some common user customizations that arrange to share new commands among running shells by manipulating the history at each prompt, and they typically include 'shopt -s histappend'; therefore, if the histappend shell option is enabled, per-session history is disabled by default. You may explicitly enable it by setting SHELL_SESSION_HISTORY to 1.

Note that, although you can disable the entire session-state restoration mechanism by creating ~/.bash_sessions_disable, this is unnecessary just to disable the per-session command history feature, and is not recommended.

If you startup a new Bash session manually (i.e. bash -xl), you can see what is run on login.

You'll see the following line in the output:

....
+++ '[' '!' -e /Users/username/.bash_sessions_disable ']'

You can create a .bash_sessions_disable file in your home directory to disable this functionality.