Just found out what to do. As you go towards the big room with the shuttle, there are 2 people standing in the corridor at the entrance. One is a man with a goatee and the other a strange fish guy with a white coat. The goatee guy is called Republic Commando and despite having no quest triangle above him he still shows that conversation icon when you hover over him. Simply fire up a conversation and you'll get a quest letting you board the ship. Hope that helps