Observations of apparent neutron bursts from air shower cores interacting in soil have been recently reported. The primary mechanism for neutron bursts, which show up as anomalous long-duration counts in a detector, is the production of evaporation neutrons from air shower cores that enter the ground in the vicinity of a detector. Neutron monitors are ground-based detectors that observe the primary cosmic ray flux in the GeV range, allowing them to be sensitive to neutron bursts. Neutron bursts could produce an unwanted background that should be taken into account in spectral studies using neutron multiplicity. We report on a simulation study of neutron bursts from air shower cores interacting in ice and discuss the implications for spectral studies done with the South Pole Neutron Monitor. We use FLUKA, including a detailed simulation of the atmosphere, snow, and neutron detectors at the South Pole.