A possibly related Q&A: Does halfling luck apply to death saving throws?
The description of the Bane spell reads (emphasis mine):
Whenever a target [...] makes an attack roll or saving throw before the spell ends, the target must roll a d4 and subtract the number rolled from the attack roll or saving throw.
The description of the bless spell reads similarly.
Based on this text, and the linked question, am I right to assume that these spells apply to death saving throws?
Death saving throws are a type of saving throws (right there in the name)†, so bane and bless can affect them. The spells also don't end because the target is at 0 hit points. The only exception is if you are the one casting the spell, because the falling unconscious that happens before making death saves would break your concentration.
† For completeness: Death saving throws are defined on page 197 of the PHB, which opens:
Whenever you start your turn with 0 hit points, you must make a special saving throw, called a death saving throw, [...]
