TM 0 Magical Soul (Costs no points)
TM 1 Mana Arrow (Learn for 1 point, you don't have to keep it at 1 but mind your mana pool and save 5 points so you can learn Invincible Casting instantly at TM 10)
TM 10 Invincible Casting (Learn Passive for 5 points)
TM 10 Cure (Learn for 1 point and Level to 10, Total of 10 points; Level 10 heals you for 24% of your health, master heals you for 30%, keep it at 10 for now)
TM 20 Bottle of Mana (Learn for 2 points, keep this at Level 1; prerequisite for Mist of Mana)
TM 40 Mist of Mana (Learn for 4 points & Master for 3 points, Total of 16 points; Learn and Master instantly)
TM 50 Arrow Rush (Learn for 4 points & Master for 3 points, Total of 16 points; Learn and Master as soon as possible right after mastering Mana Arrow & Mist of Mana)
Note: You should start saving points by TM 24 since you need 16 points to master Mist of Mana at TM 40. You need 5 points for Invincible Casting & 2 points for Bottle of Mana so that leaves you with 17 points to allocate between Mana Arrow and Cure. Master Mana Arrow after Mist of Mana. After mastering Mana Arrow, you then master Arrow Rush. You should have mastered Mist of Mana, Mana Arrow and Arrow Rush by TM 61. By this time you'd have your Cure to Level 10 already. Bards may be known for their AoEs but in my opinion, it's better to have a very strong single-target damaging spell early which is why we master Mana Arrow & Arrow Rush right after Mist of Mana. Besides, unless you can afford myshop equipment (and compound them), you wont be able to 1HKO most monsters with Wind Blade/Electro Attack/Cleaving Terra, at least not until around 100+.
TM 55 Electro Attack (Learn for 2 points & Master for 2 points)
TM 90 Electroshock (Learn Passive for 2 points; this roots/snares the monsters/players you attack with Electro Attack)
TM 20 Mana Ring (Learn for 2 points, keep this at level 10, it's a prerequisite for Incinerate)
TM 110 Incinerate (Learn for 3 points; keep this at level 10 as a prerequisite for Phoenix Rising, once you get Phoenix, you wont be using this skill as much so you don't need to Master it)
TM 140 Phoenix Rising (Learn for 3 points & Master for 3 points; this is pretty much an AoE Hell Fire meaning it's a Damage over Time skill, it's extremely powerful and lasts up to 15 seconds at Master, in my experience the maximum targets hit is 3)
TM 145 Tesla Field (Learn for 3 points & Master for 3 points; this is the second best AoE in the game for grinding--maybe I'm just biased since I really like the Fire/Electric skills--but seriously though, it has a cooldown of 4 seconds and is pretty much the same as Scorching Earth, keep in mind that if the monster you target with the skill dies, the skill duration ends, so it's best to cast this on high HP/MD targets to keep the skill going for the longest time possible which is 16 seconds at Master--yes, you can have at least 3 Tesla Fields on at the same time!)
Note: Whirlwind Blaze isn't that useful. It works the same way as Drip Bomb and Arrow of Light. You'll be getting Incinerate and Phoenix Rising anyway, and it's not a prerequisite for any skill except Dragon Storm so I suggest you skip it all together unless you're going to take the Soul Master path. It is quick cast though and is on a 2.5 second cooldown which is good for grinding. So it's really up to you whether or not you're willing to invest points into a skill that will help you grind faster but become obsolete later on in the game as you level.
Note: You'll be stuck with Electro Attack for quite a while if you decide not to get Whirlwind Blaze in this version since Scorching Earth (one of the best AoEs in the game) has not been released yet. If you ask me, the struggle is worth it in the end.