The present invention provides a reclosable bag that is substantially impermeable to oxygen by using a nylon layer in the bag side wall material. A preferred embodiment uses a bag wall comprised of low density polyethylene (LDPE) and nylon. LDPE and nylon layers are laminated together. When used as a baby bottle liner, the bag is constructed and arranged to fit into a cavity of a baby bottle. The bag includes a continuous, profiled, elongated reclosable fastener. The continuous, profiled, elongated reclosable fastener has a first continuous elongated profile strip and a second continuous elongated profile strip. The first continuous elongated profile strip and the second continuous elongated profile strip are dimensioned to provide an airtight and/or watertight seal upon interconnection thereof. The fastener provides an airtight and watertight side seal at each end of the reclosable fastener. Each side seal connects an end of the reclosable fastener to an inside surface of a front wall and an inside surface of a back wall of the liner.