To find the unit price per bottle of water, you divide the total price by the number of bottles in the case.
\[ \text{Unit Price} = \frac{\text{Total Price}}{\text{Number of Bottles}} = \frac{3.60}{24} \]
Calculating that gives:
\[ \text{Unit Price} = 0.15 \]
So, the unit price is $0.15 per bottle.