This only works with Xbox 360 version of the game
The way reserve leaders learn arts is by the way your Rush acts in combat. If Rush uses Combat Arts, your reserve leaders will learn Combat Arts, if he uses Mystic Arts, your reserve leaders will learn Mystic Arts, if he uses Item Arts your reserve leaders will learn Item Arts. The more Battle Chain you have the faster they learn the arts.
Therefore the most efficient way of levelling arts without raising Battle Rank too much is fighting low level enemies using only Rush at Ruins of Robelia Castle - Sweeping Safehold or Blackdale - The Speckled Chasm. Use Blackdale only if for some reason you hate Robelia Castle. Once all the enemies are cleared in the area, go to a different zone and save and reload to respawn the enemies.
Make sure that Rush will start every battle with sufficient AP to use whatever arts you're training. Marked Mirrorglass is a good item to raise his AP, and until you get arts high enough to drop their AP costs by just a few AP, consider using the Orb Formation. If the Rubber Soul has already been given to Glenys, then other similar accessories that grant the AP Charge on Damage effect can be used to help with Rush's AP supply.
A very useful item to equip here is the Rubber Soul. It not only restores Rush's AP a little every time he hits, but it increases the rate Weapon Type levels go up. Also note that chains higher than 370 make leaders learn skills twice as fast, so combine with Rubber Soul for best effect. When training Mystic Arts, also allow Rush to use an Imperator's Shield, as this not only has an additional AP cost cut but further increases the rate mystic arts are learned. Using the Ragna-rock is also recommended as it increases the EXP gained for all arts and skills by 3, and when combined with at least 370 Chain, will result in a x6 multiplier.
This trick also works with raising reserve leader's stats when your BR is already really high, though it will take some effort before results can be seen. A higher Chain will help with increasing EXP gained towards their stats.
The downside of this trick is that you are likely to stuff up Rush's class if you want a specific class and are not careful with what skill Rush uses.
Also another method for skill and stat grinding is to fight Bandits. This is good for end game when you have a high BR.