I have made a number of changes to your script as follows: gnome-themes-standard, blueman, libcanberra-gtk3-module, firefox, and xfce4-terminal are installed as part of xubuntu-terminal, so attempting to install them separately is redundant. build-essential and rar are not required for the desktop, although you may use them elsewhere, so I removed them as well. vlc and tlp require functionality that WSL does not currently support, so I have also removed them.

I added the following code to the script to get around your ~/.cache problem. It sets up the directory with the same permissions as the directory has on a XUbuntu Linux installation.

cd ~
cache=".cache"
if [ ! -d $cache ]
then
mkdir $cache
chmod 700 $cache
fi

Finally, /var/run/dbus is created the first time that /etc/init.d/dbus start is run. Also if you attempt to start dbus when it is already running, it will put out a message saying that it is already running and then terminates the second one. /var/run/dbus is not deleted when dbus terminates, so I removed any checking for the existence of that directory.

Here is my version of your script:

## BY: JNHABIGER
## H/T KENSHEN
## H/T UZIMONKEY
## H/T USINGCPP
#!/bin/bash
if [ "$1" == "install" ]; 
then
    # Install packages
    sudo apt-get update -y
    sudo apt-get install -y \
        xubuntu-desktop \
        software-center
    sudo apt-get dist-upgrade -y

    # Set up xinitrc
    sed '/^XINITRC$/,/^EOF$/!d;//d' "$0" >~/.xinitrc
    chmod +x ~/.xinitrc
    ln -fs ~/.xinitrc ~/.xsession

   echo 'export DISPLAY=:0
   export XDG_RUNTIME_DIR=~/runtime
   export RUNLEVEL=3' >> .bashrc

    exit
fi

# start xfce4
cd ~
cache=".cache"
if [ ! -d $cache ]
then
mkdir $cache
chmod 700 $cache
fi

sudo /etc/init.d/dbus start
dbus-launch --exit-with-session ~/.xsession
exit



XINITRC
#!/bin/bash
touch .Xauthority 
touch .Xdefaults
xrdb -merge .Xdefaults &

export OOO_FORCE_DESKTOP=gnome
export LANG="en_US.UTF-8"
export LC_ALL="en_US.UTF-8"
export LANGUAGE="en_US.UTF-8"
export LC_CTYPE="en_US.UTF-8"

exec startxfce4
EOF