We present black hole masses and accretion rates for 182 Type 1 AGN in COSMOS. We estimate masses using the scaling relations for the broad Hb, MgII, and CIV emission lines in the redshift ranges 0.16<z<0.88, 1<z<2.4, and 2.7<z<4.9. We estimate the accretion rate using an Eddington ratio L_I/L_Edd estimated from optical and X-ray data. We find that very few Type 1 AGN accrete below L_I/L_Edd ~ 0.01, despite simulations of synthetic spectra which show that the survey is sensitive to such Type 1 AGN. At lower accretion rates the BLR may become obscured, diluted or nonexistent. We find evidence that Type 1 AGN at higher accretion rates have higher optical luminosities, as more of their emission comes from the cool (optical) accretion disk with respect to shorter wavelengths. We measure a larger range in accretion rate than previous works, suggesting that COSMOS is more efficient at finding low accretion rate Type 1 AGN. However the measured range in accretion rate is still comparable to the intrinsic scatter from the scaling relations, suggesting that Type 1 AGN accrete at a narrow range of Eddington ratio, with L_I/L_Edd ~ 0.1.