I think the easiest way to impliment BLU would be to first start with a base class that can mimic foes' abilities but does not need the RNG mechanic of possibly learning an ability by witnessing it.
For example, something like 'Savage' as a base class, which learns abilities by killing monsters and consuming or absorbing their power to evolve. Once a Savage has killed a certain number of the necessary enemy (like a Hunting Log), they learn to mimic it.
Another idea would be Tactician or Magus, which would be more mage-like and able to study the behaviors of monsters in order to utilize their abilities.
The class would depend on how they want to "theme" Blue Mage as a job as to whether it would be more beastly or more "mage".
Blue Mage as a job would then be the base class learning to harness and control the most powerful and primal of beast abilities withouy becoming a monster themselves. They could also possibly be able to augment of amplify exisiting class abilities.
As for the abilities themselves, the base Class could unlock blank ability slots at the same increments as other classes. Learned abilities could then be attuned to these slots, but would have a level range to limit them. For example, if Bomb Toss is a level 20 ability, it cannot be slotted in a level 2 slot, only in a 20+ slot.
Blue Mage would also have to possibly juggle both MP and TP based on the types of abilities they are using.
Overall, it would be a DPS class but with flexibility in melee/ranged and physical/magical damage output.