Alright, now come in my rule-reading skills acquired at playing MtG, as I heard quite many rule facets are to be read similarly in DnD5e.
Note: For simplicity, I refer to the wizard having Arcane Ward up as "you", assuming it's your character.
As you quote:
Whenever you take damage, the ward takes the damage instead.
In MtG, that means an effect change. That would override all occurrences of "target" with the ward. In DnD5e, that should translate into that for the purpose of the damage it absorbs, the ward is treated as the target.
Now let's reflect on what exactly that means. First off, you can only have your maximum hitpoints reduced by the damage that actually reaches you - for the damage taken by the ward, you're not the target.
The other results depend on how your DM handles the vampire bite. As I learned, the ward has no blood (should have been obvious to me since it's conjured), and most commonly it's a mere effect that isn't alive, however it can also be regarded as something akin to a conjured spirit, thus having something similar to life energy. Therefore, if the vampire bite is restricted to actual blood in-universe, it doesn't have any effect on the ward's life energy (if it has some in the scenario), thus its maximum hitpoints remain unchanged no matter what, and the vampire only regenerates on damage it dealt to you.
However, we're in a highly magical universe with DnD5e, and it wouldn't be much of a stretch by your DM to rule that vampires can drain something such abstract as life essence. That doesn't change much if the ward is treated as effect, since it then has no life essence anyway.
If, however, your DM also goes for the "conjured spirit" version, things look much different on that regard:
Situation 1: The ward takes all the necrotic damage and remains alive. In that case, it has a reduced hitpoint maximum afterwards.
As @PhilBoncer pointed out in the comments, the ward has a regular hitpoint maximum. That means, abjuration spells can only heal it up to the new hitpoint maximum from this point on. All effects based on the maximum hitpoints of entities, obviously including ones that refer to arcane entities, are affected as well.
Situation 2: The ward takes the full damage and dies from it. In this case, the ward's reduced hitpoint maximum can only have an impact on effects that trigger as it dies and depend on the hitpoint maximum of the entity that died.
Situation 3: The ward only takes part of the damage before it dies. Regarding the ward and effects that has an impact on, this is no different from situation 2. However, as the ward is considered the target regarding the damage it absorbs and you are considered the target regarding the remaining damage, the effect actually has more than one target, which might have an influence on abilities the vampire might have that trigger based on getting a target. If, for example, the vampire has an ability that heals 1HP of an ally of his choice every time an effect of himself, his equipment, or his actions targets an entity, because of targeting 2 entities separately, this would result into healing 2HP distributed among the vampire's allies as he chooses. That is, if your DM handles targeting that way and doesn't group the two targets into one "event of targeting".
In all three situations, the vampire would recover all of the necrotic damage dealt to you and the ward on a total.
