Let \( x \) represent the cost of each bag of potatoes. Since Serenity buys 4 bags of potatoes, the total cost for the potatoes can be expressed as \( 4x \).
According to the problem, Serenity spends a total of $31.69. She spends $4.09 on milk, so we can write the equation based on her total spending:
\[ 4.09 + 4x = 31.69 \]
To solve for \( x \), first, subtract $4.09 from both sides of the equation:
\[ 4x = 31.69 - 4.09 \]
Calculating the right side:
\[ 31.69 - 4.09 = 27.60 \]
So, we have:
\[ 4x = 27.60 \]
Next, divide both sides by 4 to isolate \( x \):
\[ x = \frac{27.60}{4} \]
Calculating the division:
\[ x = 6.90 \]
Therefore, the cost of each bag of potatoes is \( \boxed{6.90} \).