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The corset of dire witchcraft is a body slot item that grants an armor bonus of 4. It is neither armor nor shield and while regular clothing can be the target of magic vestment, it is treated as armor that grants no AC bonus.
So, if I cast magic vestment on the corset, does its armor bonus stack with the enhancement bonus granted by the spell?
The corset of dire witchcraft is not an armor, nor a shield. The fact that it grants armor bonus does not mean it becomes an armor, just like the bracers of armor do not count as armor. The armor bonus is part of the description of the magic item, which means it would also disapear on an antimagic zone.
Bracers of armor surround the wearer with an invisible but tangible field of force, granting him an armor bonus of +1 to +8, just as though he were wearing armor.
The bracers also specifically mention that they can be enhanced like armor, while the corset does not:
Alternatively, bracers of armor can be enchanted with armor special abilities.
The corset of dire witchcraft also uses the same spell as the bracers on it's creation Mage Armor, which also leads me to believe this armor bonus is part of it's magical effect, not a mundane bonus.
It is vastly accepted by the community that you cannot cast magic vestment on bracers of armor or on mage armor, for the exact same reason: the bracers are not armor, nor specify that they count as armor.
Even if they did normally stack, a magical corset or bracers is not a valid target for magic vestment, as the spell requires either a suit of armor, a shield or an outfit of regular clothing. Being magical, they are no longer mundane clothing. There are several outfits defined by the rules, but none is a corset or bracer.
Target armor or shield touched
An outfit of regular clothing counts as armor that grants no AC bonus for the purpose of this spell.
Enhancement bonuses improve the original type of bonus, they are not a different bonus type. A piece of armor that grants +1 armor bonus to AC that is affected by an enhancement bonus of +1 to this armor bonus would instead grant +2 armor bonus to AC instead.
In other words, enhancement bonuses to armor and armor bonuses are not two different bonus types.
As such, if two different effects grant an armor bonus to your character, only the highest of the two should apply, as different bonus types don't stack.
That's two different types of bonus (armor and enhancement to armor). It works the same as a +1 leather armor: +2 armor bonus from the fact it's a leather armor, and +1 enhancement from the fact it's +1 -> +3 total from this piece of armor.
The corset is not "an outfit of regular clothing" since it grants AC and other stuff. "An outfit of regular clothing" would be for example a mundane shirt, coat... something that doesn't grant any armor bonus to AC. If there wasn't this line on the spell a mage without any kind of armor wouldn't be able to reinforce his mundane robes.
