You won't be able to accept the quest for your Chocobo License until you're at level 20, and the minute you hit 20 you'll want to head to Jeuno. Jeuno is a neutral city located between all three of the nations, and getting there the first time can be daunting, as the path is full of aggressive monsters. While it's best to do this in groups, one can get there on their own ... if they're prepared. For all three paths to Jeuno, you'll want to bring items that allow you to go undetected by monsters. Silent Oil and Prism Powder can be found on the Auction House under the "Medicines" category, and you can get Scrolls of Instant Reraise from your nation's Conquest representative. While these will help, pretending you're Solid Snake is just as effective and will save you money.
From Bastok, you'll want to head through Gustaberg to Konschtat Highlands, an area you should've passed through many times now. If you haven't already, go to the Crag of Dem, that giant ceramic ruin in the center of the map, and check the crystal. This will allow you to teleport back here in the future. Head northeast to the Pashhow Marshlands exit. This is where things start to get rough.
The route through Pashhow Marshlands is pretty straight forward, but there are a lot of aggressive monsters here. Watch out for Quadavs, Goobbues and Malboros, all three of which are aggressive to sound, and Goblins, who attack on sight. You'll want to head North as much as possible, and will angle northeast towards the end into Rolanberry Fields.
Rolanberry Fields is the final area before you reach Jeuno, and is exceptionally easy to navigate: just follow the road north all the way to Jeuno. Of course, the road has a number of monsters watching it, so once again be on your guard. Quadavs and Goblins are the primary threat, which attack sound and sight, respectively.