I tried several times throughout the day with no luck.
A few minutes ago, after only 4 chains, a shiny patch appeared.
I now have a shiny female Ralts with a Modest (-Atk +Sp Atk) nature. I plan to EV train for HP and Sp Attack and eventually evolve her into a Gardevoir. [:
Congrats, that is one I would quite like to get at some point in the future.