The best place to add to PATH is not the ~/.bashrc file, but the ~/.bash_profile if it exists. If .bash_profile does not exist, the best place is ~/.profile. The ~ part is automatically expanded to be your home directory (
When you login and execute bash as the "login shell", it reads .bash_profile. If it is not found, it reads .profile. The .bashrc is NOT read in this case (unless it is explicitly called from inside .bash_profile). I rarely put anything in .bashrc; one thing that supposedly should go there are aliases if you'd like to use some.
To stay compatible with some old logon shells (like ksh88), which also read .profile, you could alternatively use a separate export line there:
Your syntax is correct for .bash_profile:
You can test it immediately, just enter one of above into your actual bash command line, and then try to see if it is recognized:
Now, as a test of your .bash_profile or .profile, login on a new session (not open just another terminal window, but really use your login and password).
To enable the same setting for all system users, change /etc/profile or /etc/profile.d, depending on your Linux flavor. This is a system-wide profile, read on each login before the ~/.bash_profile or ~/.profile.