Since macOS Catalina that zsh is the default shell. From what I could understand this was caused by a change in Bash license to GPL after version 3.
So, since version 3 of Bash is pretty old they changed the default to zsh.
Since Homebrew is not yet fully Apple Silicon compatible using Homebrew was not an option. If your Mac runs Intel a simple brew install bash will install a newer version of Bash on /usr/local/bin/bash (if you had Homebrew installed obviously). You can follow the updates for Homebrew compatibility with Apple Silicon here.
This leaves us with installing Bash the good old fashion way:
curl -O https://ftp.gnu.org/gnu/bash/bash-5.1.tar.gz
tar xzf bash-5.1.tar.gz
cd bash-5.1
./configure --prefix=/usr/local && make && sudo make install
After that is done, you just need to add Bash to your available shells:
sudo bash -c "echo /usr/local/bin/bash >> /private/etc/shells"
And make Bash the active one:
chsh -s /usr/local/bin/bash
Open a new terminal window or restart your terminal app and check with:
echo "$SHELL"
bash --version