In the equation \( y = 0.35x \), \( y \) represents the total cost and \( x \) represents the number of pieces of candy.
To find the cost of one piece of candy, we can set \( x = 1 \):
\[ y = 0.35 \times 1 = 0.35 \]
Thus, the cost of one piece of candy is $0.35.
So the answer is C. $0.35.