Missing .bash_profile and .bashrc files

I don't have .bash_profile or .bashrc files and I am definitely using the bash shell. I am using Mac OS X 10.11.1 El Capitan.

How do I permanently modify my $PATH to cut down the default values Apple ships?

.bash_profile and .bashrc do not have to exist for $PATH to work, they're for bash configuration. According to the bash docs,

When Bash is invoked as an interactive login shell, or as a non-interactive shell with the --login option, it first reads and executes commands from the file /etc/profile, if that file exists. After reading that file, it looks for ~/.bash_profile, ~/.bash_login, and ~/.profile, in that order, and reads and executes commands from the first one that exists and is readable.

• To add a path to your $PATH variable for a single terminal session, do so as follows: export PATH=$PATH:pathToYourDirectory, for multiple directories export PATH=$PATH:pathToYourFirstDirectory:pathToYourSecondDirectory ...

• To see what's in your $PATH: echo $PATH or cat /etc/paths

• /etc/paths is the file that holds your system path variables

Run man path_helper for more information.