If Sam's parents agreed to pay 25% of the cost of the new bike and they paid $65, we can set up the problem as follows:
Let \( x \) be the total cost of the bike. According to the information given, Sam's parents pay 25% of the total cost:
\[ 0.25x = 65 \]
To find \( x \), we can solve for it by dividing both sides by 0.25:
\[ x = \frac{65}{0.25} \]
Calculating \( \frac{65}{0.25} \):
\[ x = 65 \times 4 = 260 \]
So, the total cost of Sam's new bike is \( \text{$260} \).
Thus, the correct answer is \( \text{$260} \).