Open up your terminal and type
sudo gedit /usr/share/applications/bitcoin-qt.desktop
Find the following line
Exec=/usr/bin/bitcoin-qt
and replace it with
Exec=APPMENU_DISPLAY_BOTH=1 bitcoin-qt
Thank you Psy! I'm still learning my way through Linux and I'd already written this problem off as something I'd have to live with. So nice to not have to boot into Windows or OSX just to run bitcoin-qt!