So this would be how she got from Fortuna Castle to the Order's HQ. If I remember right, Gloria was present at an HQ meeting in a cutscene triggered when Nero arrives at the forest, so this must be taking place while Nero's still at the Castle.
Considering Nero has a lot of stuff to do in the castle, exploring Agnus' secret laboratory, Gloria would have had pleanty of time to make her way to HQ.
Nicely done.