Modifiers such as the "Blast Proof" mod and the unique mod on the Bomb Suit item say they grant reduced explosive damage taken. They do not reduce your explosive damage taken, and instead reduce your explosive damage dealt to enemies.

For example without any of these modifiers, my grenades deal 271 damage to enemies, and I take 600 damage from enemy grenades.

With Bomb Suit equipped, my grenade deals 27 damage to enemies, and I take 600 damage from enemy grenades.

This was tested with the Secret Recipe perk which causes my grenades to deal their full damage across the entire blast radius, so the distance of the grenade to the enemy is not a confounding factor.
Clip showing grenade dealing 271 damage without Bomb Suit's 90% reduced explosive damage taken: https://gyazo.com/edc2e83a36e93840b89472128c5a4721
Clip showing grenade dealing 27 damage with Bomb Suit's 90% reduced explosive damage taken: https://gyazo.com/1d0dfea5275678767617ac96d09135df

I tested it on my game. I can confirm that the armor appears to reduce my damage dealt by 90.  Sorry I don't have recording but I could test it again if it helps.