Alchemical Savant applies once per eligible spell
Each time you cast a spell that satisfies the requirements of Alchemical Savant, you get to add the damage bonus. In your example, the transmuted Shocking Grasp definitely satisfies these requirements, so you certainly add the bonus once. If your DM rules that Absorb Elements is also eligible for the ability, then you would also add the bonus when you roll the additional damage for this spell as well, with the final result that you roll for the normal damage of Shocking Grasp plus the normal damage of Absorb Elements plus 2 times your intelligence modifier.
However, the question of whether Absorb Elements is eligible for the damage bonus from Alchemical Savant is a surprisingly tricky one.
When does the damage bonus from Alchemical Savant apply?
One valid reading of "whenever you cast a spell" is that the damage bonus only applies to damage rolls that happen at the time of casting. If this is your DM's ruling, then Absorb Elements doesn't satisfy this requirement. On the other hand, it's an equally valid reading that the bonus you gain when casting the spell is something you hold onto and then use on the damage roll of your choice at any time during the spell's duration. This would be similar to an Illusionist wizard's Malleable Illusions, which applies "when you cast an illusion spell" but is unambiguously used during the spell's duration.
I would argue in favor of the latter, more permissive reading for Alchemical Savant. Two spells on the Alchemist Spells table, Flaming Sphere and Cloudkill, deal damage of an eligible type, but not at the time of casting. If you (or your DM) believe that these alchemist spells are supposed to get the damage bonus from Alchemical Savant, then the exact timing of the damage roll doesn't matter as long as it happens during the spell's duration. (Indeed, I've been adding the bonus to my castings of Flaming Sphere in actual play, and my DM hasn't batted an eye.)
Does Absorb Elements even have a damage roll?
You could also argue that Absorb Elements doesn't even have its own damage roll, but rather it adds additional damage to an attack. The spell says:
[...] Also, the first time you hit with a melee attack on your next turn, the target takes an extra 1d6 damage of the triggering type, and the spell ends.
This wording closely matches that used in Flame Arrows:
When a target is hit by a ranged weapon attack using a piece of ammunition drawn from the quiver, the target takes an extra 1d6 fire damage.
as well as some magic items, such as the Frost Brand:
When you hit with an attack using this magic sword, the target takes an extra 1d6 cold damage.
So it seems that this wording indicates that the damage is not a separate source of damage, but is added to the attack's damage. (This matters, for example, when determining whether the target must make one or two saving throws to maintain concentration.) If this is your DM's interpretation, then they might say that Absorb Elements is not eligible for Alchemical Savant because it doesn't deal its own damage, but rather modifies the damage of something else.
On the other hand, your DM might be perfectly satisfied with the straightforward logic that the if the text of Absorb Elements says to roll for fire damage, then the spell is the source of the fire damage, and hence the Alchemical Savant bonus applies. It's certainly a ruling that doesn't require cross-referencing multiple spells and magic items to compare their wordings.
In summary, there is ample room for a DM to rule either way on whether the additional attack damage from Absorb Elements gets the damage bonus from Alchemical Savant.
