Does gear count as a friendly unit? Would the Sprite Fountain gear itself count as a temporary friendly unit towards the "Bashful Bloom" legend's "this ability cost 1 less for each friendly unit with temporary"?

No, gear does not count as a friendly unit.

According to Rule 148.1, gear is a distinct game object and card type from units. Therefore, the Sprite Fountain gear—even though it possesses the Temporary keyword—does not count as a "friendly unit with Temporary" for the ability on the Bashful Bloom legend.

Bashful Bloom specifically reduces its cost based on "each friendly unit with Temporary." Since gear is not a unit, the gear itself is not counted by the ability, regardless of any keywords it may have.