a. Whenever any pupil lives more than one and one-half (1 1/2) miles from any established bus stop or from the school of attendance, as designated by the board of trustees, and such pupil is regularly transported by private vehicle not under contract with the school district, the board may pay to the parent or guardian an amount per month up to ten dollars ($10.00) per vehicle plus mileage at the current rate established by the state board of examiners for each round trip approved.
b.  Whenever in the judgment of the board of trustees any pupil residing within the area of a nontransportation zone, and otherwise eligible to transportation, cannot be transported in any manner herein authorized, the said board may pay to the parent or guardian thereof such amount of the cost incurred by the parent or guardian for the board and lodging of the pupil as may be authorized by the board of trustees.