To find the price per quart of a 2-gallon bottle of bleach that costs $9.36, we first need to convert gallons to quarts.
1 gallon is equal to 4 quarts, so:
\[ 2 \text{ gallons} = 2 \times 4 = 8 \text{ quarts} \]
Now that we know there are 8 quarts in 2 gallons, we can find the price per quart by dividing the total price of the bottle by the number of quarts:
\[ \text{Price per quart} = \frac{\text{Total price}}{\text{Number of quarts}} = \frac{9.36}{8} \]
Calculating this gives:
\[ \frac{9.36}{8} = 1.17 \]
Thus, the price per quart is:
\[ \boxed{1.17} \]