I am another Ubuntu 20.04 user and a recent entrant to Wolfram (free Developer Licence) so we can compare notes. I have Windows 10 and Ubuntu 20.04 in dual boot mode (Ubuntu on external bootable SSD).
You write ..
I thought I would install the WolframEngine to my WSL
Clarification is needed. There is WSL1 (the bash only version) and WSL2 (a full
instance of Ubuntu only in Windows 11). My Windows 10 does offer WSL1 (bash only) but I have not progressed to trying WSL2 (new generation for coming Windows 11). I do prefer to keep these two beasts apart (Windows and Ubuntu).
You write ..
I'm not sure why my system can't run the shell script. I'm running it
using bash, as that is the shell interpreter for my Ubuntu distro. How
can I get my system to run this file so I can start using
wolframscript from my command line?
Now in my Ubuntu session ...
sudo locate WolframEngine
/usr/local/Wolfram/WolframEngine/12.3/ .. multiple files
sudo locate WolframEngine | grep /home
/home/dl/.WolframEngine/ .. multiple files
/home/dl/Downloads/WolframEngine_12.3.1_LINUX.sh
which wolframscript
/usr/bin/wolframscript
If you run ..
wolframscript --help
you will see ..
-configure [KEY=VAL...] Configure WolframScript by specifying values for particular configuration variable keys. If no keys are given, this prints the current configuration.
-activate [KEY] Activate the Wolfram Engine through the cloud or with a key.
I recollect that I had to use wolframscript -activate [KEY] to get WolframEngine humming.
Regarding the bash script not running you might just have a permissions problem depending on where you placed the bash script. You can enable the file .. Properties > Permissions > Is executable (tick). I use Krusader file manager for such operations but you can use Nautilus or command line. However if you are in bash mode only (WSL1) you cannot use apps and you will need command line to change permissions.
Finally if you decide to experiment with Jupyter Notebooks integrated with Wolfram you can install a Wolfram Kernel into a Jupyter Notebook.
You will need to install (optionally) WolframLanguageForJupyter.
Here is a full list of Kernels.
https://github.com/jupyter/jupyter/wiki/Jupyter-kernels
Near the bottom is Wolfram Language for Jupyter
https://github.com/WolframResearch/WolframLanguageForJupyter
There is another Kernel named iWolfram which I have not tried.
And since Jupyter Notebooks allows different Kernels to ne used in a Jupyter Notebook you can experiment further with others depending on your requirements.
I am trying a mix of Kernels.
One last point, if you are in Ubuntu you can use editors which recognise the Wolfram Language.
I have as one editor Sublime Text 3 and you can install as a package WolframLanguage.
https://packagecontrol.io/search/wolfram
Here is Visual Studio Code
https://marketplace.visualstudio.com/items?itemName=lsp-wl.lsp-wl-client
Then there is Atom (but now falling behind VSCode since Microsoft acquired Atom).
https://atom.io/packages/language-mathematica
This latter page points to Wolfram Syntax which is helpful.
https://reference.wolfram.com/language/tutorial/InputSyntax.html
I try all three editors in various experiments/learning. I am experimenting with automated workflows to link Wolfram with other apps.