There have been local calls for an increase in school transport provision.
Deputy Niamh Smyth says parents in the Cavan/Monaghan region are becoming distressed because their child has been left with no ticket for the school bus.
Children and teenagers return to education this week after their summer holiday break.
Meanwhile, Deputy Smyth added that the rules within the school transport system are "too stringent" when it comes to assessing eligibility.
She says that while she accepts priority must be given to those who meet the criteria, the current situation is leaving families in "precarious circumstances".
"The announcement of free school transport by the Minister for Education has further added pressure to the school transport system," continued Deputy Smyth.
"Before this announcement was made, a review of the rules of this scheme was undertaken by Minister Foley and I welcome this move.
"But the rules are simply too stringent when reviewing children's eligibility for a bus ticket and Bus Eireann are bound to work within the framework applied by the Department when it comes to 'the nearest school rule'.
"This rule deems whether a child is eligible - attending its closest school in kilometers or concessionary - not guaranteed a ticket."
