The Blue Mage job in Final Fantasy XIV allows the player to learn new spells by defeating enemies who uses these spells, and the Blood Drain spell is one of these. You don't need to be hit by the Blood Drain spell from an enemy, but instead just kill the enemy, and each kill has a chance to teach you how to use the spell for yourself.
The enemies you need to defeat to learn Blood Drain are Cave Bats in Lower La Noscea (27, 16) or Carrion Chigoes in Lower La Noscea (27, 16). Either of these two mobs will use Blood Drain, and they both have a chance to teach you the spell upon death.
The enemies are only around level 7, so you should be able to get this spell farily early.
Blood Drain is a low-rank spell, so you have a rather high chance to learn it upon killing the mobs. This means that it should not take you too long to learn the spell if you farm Cave Bats or Carrion Chigoes.