We present a modified optical luminosity-HI mass bivariate luminosity function (BLF) based on HI line observations from the Nancay Interstellar Baryons Legacy Extragalactic Survey (NIBLES), including data from our new, four times more sensitive follow-up HI line observations obtained with the Arecibo radio telescope. The follow-up observations were designed to probe the underlying HI mass distribution of the NIBLES galaxies that were undetected or marginally detected in HI at the Radio Telescope. Our total follow-up sample consists of 234 galaxies, and it spans the entire luminosity and color range of the parent NIBLES sample of 2600 nearby (900<cz<12000km/s) SDSS galaxies. We incorporated the follow-up data into the bivariate analysis by scaling the NIBLES undetected fraction by an Arecibo-only distribution. We find the resulting increase in low HI mass-to-light ratio densities to be about 10% for the bins -1.0<=log(M/L)<=-0.5, which produces an increased HI mass function (HIMF) low mass slope of {alpha}=-1.14+/-0.07, being slightly shallower than the values of -1.35+/-0.05 obtained by recent blind HI surveys. Applying the same correction to the optically corrected bivariate luminosity function from our previous paper produces a larger density increase of about 0.5 to 1dex in the lowest HI mass-to-light ratio bins for a given luminosity while having a minimal effect on the resulting HIMF low mass slope, which still agrees with blind survey HIMFs. This indicates that while low HI-mass-to-light ratio galaxies do not contribute much to the one-dimensional HIMF, their inclusion has a significant impact on the densities in the two-dimensional distribution.