Preventing Termination of Utility Services in Bankruptcy Act of 2014 - Amends federal bankruptcy law, with respect to the prohibition against disruption of utility services to a debtor, to declare that an individual debtor may not be required to furnish assurance of payment if he or she pays, within 20 days after the date of the order for relief, those debts owed to a utility for service during that period, and afterward also pays when due debts owed for service during the pendency of the case in bankruptcy.