Concrete Pump Tax Fairness Act This bill amends the Internal Revenue Code to: (1) impose a mileage-based user fee on owners of mobile mounted concrete boom pump vehicles, (2) allow a credit against the fee for certain fuel taxes and other specified taxes that currently apply to the owners of the vehicles, and (3) require the revenues from the fee to be deposited into the Highway Trust Fund. A "mobile mounted concrete boom pump vehicle" is a vehicle that is mobile machinery and on which the mounted machinery consists of a concrete boom pump and related subordinate parts.