Does anyone know how many frames of blockstun a shielded bomb puts your opponent into?
That depends. <- The greatest of answers, and a sure sign that you're not about to like what follows.
If we're just talking about the bomb itself being shielded, then there are zero frames. In context this obviously wasn't the information you were after, but it's good to be clear about these things.
So we're talking about the explosion generated by the bomb.
But then the amount of blockstun inflicted will depend on how much damage the explosion would have otherwise done, and this in turn depends on e.g. how fast the bomb was moving at the time it exploded. In context however it would seem you are after how much blockstun it inflicts when the timed fuse runs out while being held, i.e. the least amount.
But then there's something else to consider as well. When talking about hitboxes that are disconnected from your own body (items and projectiles), the amount of 'time spent in shield unable to do anything' should consist not only of blockstun but also block-freeze (i.e. shield hitstun and shield hitlag respectively if you're more familiar with those terms). If we were talking about e.g. a normal Jab hitting a shield, we wouldn't really care about the block-freeze because both we and our opponent have to wait out the same time, and we only start to gain an advantage of some sorts when talking about blockstun, during which we continue the animation of our move while they are still stuck in shield. This is why disembodied hitboxes like projectiles are so good against shields, because the attacking character doesn't freeze during blockfreeze. To counteract this brokenness they used a different shield stun formula for projectiles to reduce the amount of shield-stun given, but it's still a significant point to bring up.
But then the context you're referring to is talking about either dodging the explosion or perfect shielding it, and I should note at this point that perfect shielding isn't as effective as you might think. The greatest advantage it gives is freeing up your standard options (minus walking/dashing) without having to wait through the 7 frames of shield-drop, but in terms of comparing a regular OoS option such as grab when used out of a regular shield or when used out of a perfect shield, the difference is unimpressive at best. This is because a perfect shield only reduces around a quarter of the blockstun inflicted. So to take an example, if Link shields Mario's D-tilt with a standard shield, he will endure 6 frames of blockfreeze then 4 frames of blockstun and be able to start his grab on frame 11. But if Link powershields Mario's D-tilt he will still endure 6 frames of blockfreeze then 3 frames of blockstun and be able to start grab on frame 10. Normally because blockfreeze doesn't matter so much, this is still a semi-decent gain from 4 frames to 3, but when talking about disembodied hitboxes it becomes a lot worse (as it would have been a gain from 10 to 9).
With all of that in place, let's look at exactly how many frames you would be able to move before the opponent can due to powershielding the timed explosion of a held-bomb where they only shield it normally.
And the answer is 1. You can act 1 frame earlier only. Granted, you can use any grounded option immediately instead of being restricted to OoS options, but still. Considering Link's slower frame data, this is a dumb idea. End of story.