If you set up an enemy to ignore bombs, it ignores bomb explosions.
However, if you give the enemy shields, and the shield is hit by a bomb (keeping in mind all the directionality stuff that entails) - it will flash and be knocked back by bombs, even if it is set to ignore them.
As far as I can tell, they do not take damage from this.
That is by design. In general, bombs as objects have no damaging properties: Only the explosion does, so, of course only the explosion damage is used when calculating the defences.
The knockback direction is also intentional with respect to shields. If you want us to add rules to ignore shields, or to ignore knockback, that needs to be a feature request.
IOW, this is not a bug. It is a known engine effect that was intentionally included to mimic classic Zelda games.