most efficient way to level DPS classes

[Bixby]

Think I might try doing FATE/dungeon queue until I get my first low level roulette done then do leves but can you do leves with a chocobo out?

You can do normal (non-GC) leves with a chocobo, but not GC leves.

Whether battle leves are worth it vs. FATEs depends on a few things. There are some leves where you can dash through them and ignore a lot of the mechanics/enemies to turn them in quickly. For example, the collect-the-bottles leve in Costa del Sol. Enemies spawn every time you collect a bottle, but you can just run to the next bottle, pick it up, and move on before the enemy can even hit you. It makes for decent XP/hour, especially since you can do it with the maximum +level difficulty right from the start.

Most leves where you actually have to fight are not that great. If there are other people around doing FATEs, FATEs are almost certainly better. If you'd be pretty much soling FATEs, cheesing the leves you can cheese through might be better.