Does the Invulnerability spell protect me from the shared damage of the Warding Bond spell?

Question

As a Wizard, I can cast Invulnerability (XGtE, p. 160) on myself, which states:

You are immune to all damage until the spell ends.

If I then cast Warding Bond, do I suffer the reflected damage when the warded creature takes damage?

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Further information about my build:

I intend to go for a 3 cleric (tempest domain) / 17 wizard (abjuration).

High constitution / intelligence, heavy armored with a shield.

As spells, I'll use Bless and Warding Bond, with high-valued Arcane Ward (avoiding most of concentration checks) which I refill with Abjuration spells (absorb elements, shield, counterspell, banishment), and eventually a Chain Lightning with Destructive Wrath for a 240 damage spell once a day.

At last, I can use Mind Blank (level 8) to give immunity to physical damage to an ally (with concentration) and Invulnerability (level 9) to grant resistance to all damage to an ally with Warding Bond while being immune to that damage.

I can use Ability Score Improvements to easily max Constitution and Intelligence, along with Resilient, Armor Master (to reduce damage taken from warding) or War Caster and Shield Master feats if I'd find a giant belt to melee fight, unleash high-level absorb elements and shove with shield as bonus action.

In my party is a cleric, and with a ring of spell storing I could spare the cleric levels to get to 19 wizard levels and 1 fighter level (to get heavy armor proficiency, Protection fighting style and full ability score improvements) and bond warding with it, but I don't want to rely on magic items too much

Answer 1

Invulnerability prevents damage from Warding Bond

As you note, Invulnerability states:

You are immune to all damage until the spell ends.

And Warding Bond states:

Also, each time it takes damage, you take the same amount of damage.

There is no reason for the caster's immunities not to apply to this damage. Several features that ignore immunities state so (see the Evocation Wizard's Overchannel that states "This damage ignores resistance and immunity.", for example) but Warding Bond does not say that it ignores immunities so it doesn't.

The strategy of connecting to several different creatures with Warding Bond may be possible, as is discussed in this related Q/A¹

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^{1. Pointed out by András, this is contrary to my first reading of Warding Bond}