This is how I solved the issue with the provided steps:
Install Homebrew from the docs on their homepage
Install Git using Homebrew (optional, but nice to have a more up-to-date git)
brew install git
Now install bash:
brew install bash
Add this install of bash to the allowed shells list:
echo '/usr/local/bin/bash' | sudo tee -a /etc/shells;
Homebrew installs things to /usr/local/Cellar/ by default, then symlinks any binaries to /usr/local/bin, so you've now got the latest bash sitting at /usr/local/bin/bash
Finally, change your shell to use this new one:
chsh -s /usr/local/bin/bash
Open a new terminal window/tab, and run these commands to double-check your work:
$ echo $SHELL
/usr/local/bin/bash
$ echo $BASH_VERSION
5.1.8(1)-release
This also solved the issue for running the source ~/.bash_profile
whenever I open a new window in the terminal.
Reference:
The answer is from here How do I install Bash >= 3.2.25 on Mac OS X 10.5.8? by user jeffbyrnes