How to do `omz update` as part of my bash script?

I'm writing a bash script to update oh-my-zsh & plugins. file: update_omz_plugin.sh:

#!/bin/bash
ZPLUGINDIR=$HOME/.oh-my-zsh/custom/plugins
ZTHEMEDIR=$HOME/.oh-my-zsh/custom/themes

if cd $ZPLUGINDIR/fast-syntax-highlighting; then git pull; else git clone https://github.com/zdharma-continuum/fast-syntax-highlighting.git $ZPLUGINDIR/fast-syntax-highlighting; fi

if cd $ZTHEMEDIR/powerlevel10k; then git pull; else git clone https://github.com/romkatv/powerlevel10k.git $ZTHEMEDIR/powerlevel10k; fi

omz update

However, if I do bash update_omz_plugin.sh, I got

update_omz_plugin.sh: line 9: omz: command not found

I thought this is because omz is a function defined in source $ZSH/oh-my-zsh.sh? How can I update my script to solve this issue, i.e., make omz update work?

Solution

I ran into this question when looking for why my script that updated omz was resetting and executing twice. For whomever it may help, the (current) OMZ FAQ has a section just for this: how-do-i-manually-update-oh-my-zsh-from-a-script:

The best way to do that is to call the upgrade.sh script directly. If $ZSH is defined (it should point to where OMZ is installed), then you can call it like so:
"$ZSH/tools/upgrade.sh"
The omz update command ... restarts the zsh session (which might cause a restart loop).

Of course, in order to have $ZSH set you should be running in a zsh script as per the accepted answer by Robby Russel; Although I suppose you could manually resolve it to /Users/my-user/.oh-my-zsh or whatever.