In the function \( f(x) = 10x + 15 \), the total cost \( f(x) \) consists of two parts: the hourly fee and the flat rate. The hourly fee is represented by \( 10x \), where \( x \) is the number of hours the bicycle is rented at a rate of $10 per hour.
The term \( 15 \) in the function represents the flat rate, which is the cost charged regardless of how many hours the bicycle is rented.
Therefore, the flat rate for the bicycle rental is $15.