How do I install bash shell in Alpine Linux?

It is easy to have bash installed but this does not mean the symlinks to busybox are gone. The syntax is as follows with apk command
# apk update
# apk upgrade
# apk add bash
Sample outputs:

(1/5) Installing ncurses-terminfo-base (6.0-r7)
(2/5) Installing ncurses-terminfo (6.0-r7)
(3/5) Installing ncurses-libs (6.0-r7)
(4/5) Installing readline (6.3.008-r5)
(5/5) Installing bash (4.3.48-r1)
Executing bash-4.3.48-r1.post-install
Executing busybox-1.26.2-r5.trigger
OK: 14 MiB in 21 packages

How to install bash man pages and other docs

To install bash documentation, enter:
# apk add bash-doc
To install bash automatic command line completion install, run:
# apk add bash-completion
Sample session:

How to set bash as login shell

To use bash as a shell just type bash:
$ bash
To login to alpine Linux LXD vm from host, enter:
$ lxc exec alpine-lxd-vm-name-here bash
One can change root shell to bash shell using the following method:
# vi /etc/passwd
Find user name and the default shell such as /bin/ash:

root:x:0:0:root:/root:/bin/ash 

Replace it with /bin/bash:

root:x:0:0:root:/root:/bin/bash

Customize bash shell

Here is a sample file:
cat ~/.bashrc
Sample outputs:

alias update='apk update && apk upgrade'
export HISTTIMEFORMAT="%d/%m/%y %T "
export PS1='\u@\h:\W \$ '
alias l='ls -CF'
alias la='ls -A'
alias ll='ls -alF'
alias ls='ls --color=auto'
source /etc/profile.d/bash_completion.sh

See Customize the bash shell environments wiki page for more info.

Conclusion

You learned how to install bash shell on Alpine Linux along with documents, man pages and configure the bash shell as per your needs. I suggest you read bash man pages/docs here online for more info.