The ARIANNA experiment seeks to observe the diffuse flux of neutrinos in the 108-1010 GeV energy range using a grid of radio detectors at the surface of the Ross Ice Shelf of Antarctica. The detector measures the coherent Cherenkov radiation produced at radio frequencies, from about 100 MHz-1 GHz, by charged particle showers generated by neutrino interactions in the ice. The ARIANNA Hexagonal Radio Array (HRA) is being constructed as a prototype for the full array. During the 2013-14 austral summer, three HRA stations collected radio data which was wirelessly transmitted off site in nearly real-time. The performance of these stations is described and a simple analysis to search for neutrino signals is presented. The analysis employs a set of three cuts that reject background triggers while preserving 90% of simulated cosmogenic neutrino triggers. No neutrino candidates are found in the data and a model-independent 90% confidence level Neyman upper limit is placed on the all flavor ν+ν¯ flux in a sliding decade-wide energy bin. The limit reaches a minimum of 1.9×10-23GeV-1cm-2s-1sr-1 in the 108.5-109.5 GeV energy bin. Simulations of the performance of the full detector are also described. The sensitivity of the full ARIANNA experiment is presented and compared with current neutrino flux models.