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Check your environment. idea.sh needs a couple of variables (IDEA_JDK or JDK_HOME) defined to work correctly. They may be defined for your shell, but not for the X11 session. Try defining these variables in your ~/.profile script, then logging out and in again. Another option is hardcoding these variables in the idea.sh script. This is guaranteed to work, but then you have to do it every time you upgrade.

I hadn't thought about the difference between the shells, thanks!
I've been working on a script to install an icon in the menu automatically.
It would live in the bin directory and so far looks like this.

The problem is getting the environment variables in correctly.
I don't want to sync up my .bashrc and .profile all the time (or ever) so I thought about  creating an extra launcher script that contains the necessary paths from the current env then calls the idea.sh.
Of course the other option would be do just push these into the idea.sh
I'm not sure what is the best option.

#!/bin/bash
#

#Get directory that the script resides in (should be the idea bin directory)
CurrentDir="$(cd "${0%/*}" 2>/dev/null; echo "$PWD")"

#Create launcher with env variables in it
Launcher="launcher.sh"

#Check that at least one of these variables exists
if [ -n "$IDEA_JDK" -o -n "$JDK_HOME" -o -n "$JAVA_HOME" ]; then
    echo "#!/bin/bash" > $Launcher

    if [ -n "$IDEA_JDK" ]; then
      echo export IDEA_JDK=$IDEA_JDK >> $Launcher
    fi
    if [ -n "$JDK_HOME" ]; then
      echo export JDK_HOME=$JDK_HOME >> $Launcher
    fi
    if [ -n "$JAVA_HOME" ]; then
        if [ -z "$JDK_HOME" ]; then        
            echo export JDK_HOME=$JAVA_HOME >> $Launcher      
        fi
        echo export JAVA_HOME=$JAVA_HOME >> $Launcher
    fi
    echo "exec $CurrentDir/idea.sh" >> $Launcher
    chmod +x $Launcher
else
    echo "No JDK found to run IDEA. Please validate either IDEA_JDK or JDK_HOME points to a valid JDK installation"
    exit 0
fi

#Create a shortcut in the Programming Menu
FileName="/usr/share/applications/idea.desktop"
echo "[Desktop Entry]" |sudo tee $FileName
echo "Encoding=UTF-8" |sudo tee -a $FileName
echo "Name=Intellij IDEA" |sudo tee -a $FileName
echo "Comment=Develop With Pleasure!" |sudo tee -a $FileName
echo "Categories=GNOME;Application;Development;" |sudo tee -a $FileName
echo "Exec=$CurrentDir/$Launcher" |sudo tee -a $FileName
echo "Icon=$CurrentDir/idea128.png" |sudo tee -a $FileName
echo "Terminal=false" |sudo tee -a $FileName
echo "Type=Application" |sudo tee -a $FileName

Remember that bash also reads your ~/.profile, so you can move everything that's currently in your ~/.bashrc to ~/.profile, unless it's something that actually should only be defined for interactive bash shells.