I've been steadily leveling mine just by leveling my side jobs. I do my leve/fate challenge logs on a non-70 and bring my chocobo with me. Gets the 100 kill done every single time.
Then off to the stables until the next week and I train it whenever I can (and hope my FC mates do too).

It reached 19 recently so I'm very excited. Probably in a month it'll be 20 \o/

I didn't start playing seriously (more than an hour a week) until 4.1 so that's about a year.