The spirit's attack does 0 damage plus life stealing. A damage value of 0 is still considered damage for the purposes of skills and effects that trigger when the target takes damage.
Unlike most spirit attacks, the Bloodsong attack does not have a specific activation time, so it uses the Spirit of Blood Song's natural attack speed, which is approximately 1 attack every 1.75 seconds.
Since this spirit heals itself, it can make a good battery for skills like Spirit Transfer.
Anomaly! This skill used to be named Blood Song, and the spirit hasn't been updated: The summoned spirit is called Spirit of Blood Song.