Distance measurements using Type Ia Supernovae have enabled the startling discovery that the expansion of the universe is accelerating. To determine the nature and the source of this acceleration, systematic uncertainties on distance measurement must be reduced. Due to their importance to high-redshift optical SN Ia cosmology and their sensitivity to dust and progenitor metallicity effects, understanding rest-frame near-UV (NUV) measurements of Type Ia SNe is key to reducing these systematic uncertainties. Unfortunately, the calibration and acquisition of this data is challenging. We use direct comparisons of low-redshift SDSS-II and Carnegie Supernova Project NUV SN Ia photometry to quantify uncertainties on our ability to calibrate observer frame observations, and find that photometry in this region is consistent at the level of 2% in flux with a 6% scatter about the mean. Monte Carlo simulated SN Ia samples are used to directly measure Hubble Diagram biases resulting from SN Ia model training. Four simulated SN Ia samples are used to train the SALT-II SN Ia model: two width-luminosity adjustments and two intrinsic scatter models are tested. Adding intrinsic scatter to the training sample yields biased color laws and wavelength-dependent scatter in the NUV region, and causes the color correction parameter β to be systematically underestimated. Assuming a flat ΛCDM cosmology and including BAO and CMB constraints, three of our tests correctly recover the Dark Energy equation of state parameter w. The fourth test gives a w offset of 0.02, with a 4-σ significance. The software developed to support this work may be adapted to measure Hubble Diagram biases for any combination of SN Ia model and surveys.