The function \( f(x) = 10x + 15 \) models the total cost of renting the bicycle, where \( x \) represents the number of hours rented. In this function, the term \( 10x \) represents the hourly fee ($10 per hour), while the constant term \( 15 \) represents the flat rate for the bicycle rental.
Therefore, the flat rate for the bicycle rental is $15.