The function given for the cost of the bicycle rental is \( f(x) = 10x + 15 \), where \( x \) is the number of hours rented. In this function, \( 10x \) represents the hourly cost (which is $10 per hour), and the constant term \( 15 \) represents the flat rate charged for renting the bicycle.
Thus, the flat rate for the bicycle rental is $15.