Spells like Bless and Bane improve your ability checks based on the roll of a die. The question is, how do these skills affect your passive skills?
Let's say your passive perception is 14, and you were blessed. Do you now have a flat +2.5 to that, or would the DM have you roll a 1d4 any time they want to use your passive perception?
Neither will affect passive ability checks. Besides the fact that neither bane nor bless does not cover ability checks, passive checks are raw values and the only thing that will affect the score is advantage or disadvantage with will add or subtract 5 respectively. The description of passive checks clearly outlines what affects them:
Passive Checks
A passive check is a special kind of ability check that doesn’t involve any die rolls. Such a check can represent the average result for a task done repeatedly, such as searching for secret doors over and over again, or can be used when the DM wants to secretly determine whether the characters succeed at something without rolling dice, such as noticing a hidden monster. Here’s how to determine a character’s total for a passive check:
10 + all modifiers that normally apply to the check
If the character has advantage on the check, add 5. For disadvantage, subtract 5. The game refers to a passive check total as a score. For example, if a 1st-level character has a Wisdom of 15 and proficiency in Perception, he or she has a passive Wisdom (Perception) score of 14. The rules on hiding in the “Dexterity” section below rely on passive checks, as do the exploration rules in chapter 8.
For reference, the specific text of Bless is:
Bless
You bless up to three creatures of your choice within range. Whenever a target makes an attack roll or a saving throw before the spell ends, the target can roll a d4 and add the number rolled to the attack roll or saving throw.
and the specific text of bane is:
Bane
Up to three creatures of your choice that you can see within range must make Charisma saving throws. Whenever a target that fails this saving throw makes an attack roll or a saving throw before the spell ends, the target must roll a d4 and subtract the number rolled from the attack roll or saving throw.
This is something for your DM to decide. While the spells have "an attack or saving throw" in their descriptions DMs are expected to bend the rules of these spells and apply them as they will in game. Therefore your question is best posed to your DM or if you're the DM yourself you should think about how you want the spell to work in your campaign and keep track of your PCs using it
