The bonus to damage from Enhanced Bond is not a damage roll of the spell.
The official wording of Enhanced Bond printed in Tasha’s Cauldron of Everything1 says:
Whenever you cast a spell that deals fire damage or restores hit points while your wildfire spirit is summoned, roll a d8, and you gain a bonus equal to the number rolled to one damage or healing roll of the spell.
Enhanced Bond is a bonus that gets added to one damage roll of the spell, but it is not itself a damage roll of the spell. Since it is not a damage roll of the spell, the roll for Enhanced Bond is not eligible for Elemental Adept, which requires:
you roll damage for a spell you cast
This ruling is further established by the fact that the roll for Enhanced Bond occurs the moment the spell is cast, prior to any attack roll or saving throw occurring, so it is definitely not part of the damage roll, which only occurs after a successful attack roll of failed save (in most cases).
1 The wording in the question matches the wording found in the Unearthed Arcana version of the Wildfire Druid, but the difference in wording does not affect the logic of this answer.