It took me months to get to 20 with my white mage. But that's just cause I used to play for only a few hours every week or two and I focused on Rank more than I did on leveling. If you play everyday it should take you no more than a few weeks. In fact, I know someone who took white mage to 30 in less than 2 weeks.

The first 10 levels are killer, especially the level 8-10 grind. But once you start partying, it should be extremely easy for you to find exp parties and get to 20.