Skill ups against appropriately-higher level mobs are Always faster than skill ups on yourself.
Blue magic, I would imagine, would be fastest skilled up while performing blue magic on higher leveled mobs- try doing an abyssea exp party, get some refresh atma, and even with a few MP cheap spells you'll start seeing major skill ups.

I do hope that S.E. notices that skill ups don't occur as fast as they've made leveling, what with fields of valor exp, and later with abyssea- and soon to be their new mid-range to high-end leveling with valor-like rewards, players need competent skill as they progress, more often skill ups, please!

btw, as a bard... go /rdm an equip all that great fast cast and -song casting gear you have, spam threnody in your downtime, or if you're too busy pulling... Etudes are the way to go. Spam etudes with the right instrument for an hour or so, and you should see significant skill ups.

My personal struggles are Dark Magic, Enhancing Magic, Healing Magic, and Holy Magic.
Dark Magic is used maybe twice on average per mob (if I'm lucky..) Enhancing Magic seems to skill up when I'm Not trying- IE: Teleport skill ups proc more often than me sitting and spamming bar-spells. Holy Magic, I've gotten into the habit of tossing Banish and Flash as often as I can afford to- on the pretense that it provides a short defense down on the mob or knocks its accuracy down to near zilch. :P But still, skilling those up kills me inside...