The Blood Suckler and its cousin the Bone Suckler are both kamikaze Suckler ANMCs, meaning that they self destruct when they get too close or die. They are found mostly in Dryfield during the night and replace most of the Bone Sucklers when playing through Bounty / Nightmare mode.
Like their cousins, the suckler will crawl over to Aya. They will attempt to grab her leg for some minor damage, then detonate. Fortunately, there is a bit of lead time before this happens, so as long as the player stays on the move, they cannot grab Aya's leg. To avoid taking any damage from them, shoot them from a distance, since their explosive attack has a considerable radius.
Since their explosion can also damage other NMCs (for 80-95 damage on Normal/Replay), this can be useful in wiping out multiple groups of sucklers or damaging Scorpions, Scavengers or Strangers (which can take extra damage from an explosion) that are in the vicinity.
After a while of idle movement / chasing Aya, it will eventually stop chasing her and fall asleep for a while.
While it is never shown in game, these are the children of the Mind Suckler and theoretically they could develop into the more advanced version.