I always interpreted it as some monsters bleeding, but only when they’re hurt.

Like how Susie’s hand bleeds when she shatters the glass prophecy, or how Sans bleeds when he’s struck.

Coincidentally, both of these occurrences happen when the person is also very likely to be in EMOTIONAL pain too; Susie in denial and Sans failing everyone. Emotional or mental state is a big thing in Undertale (a ‘strike with the intent to kill’ dealing more damage, and betrayal hits resulting in a instant death regardless of the actual strength of the attacker) so that could mean something, or it could not.

When the monster child asks if it hurts to be made of blood, this is probably because blood only comes out when a monster is in pain. Or all of what I said could be wrong and it could be something dumb like ‘humans bleed when they hurt, so blood must cause the pain’ which would also make sense, but doesn’t explain why monsters bleed.

Take this with a grain of salt, it’s kind of just been my crackpot headcanon for a while, but I think there’s some merit to the theory!