We make use of sensitive (9.3 mu Jy beam(-1) rms) 1.2 mm continuum observations from the Atacama Large Millimeter/submillimeter Array (ALMA) Spectroscopic Survey in the Hubble Ultra-Deep Field (ASPECS) large program to probe dust-enshrouded star formation from 1362 Lyman-break galaxies spanning the redshift range z.=.1.5-10 (to similar to 7-28 M-circle dot yr(-1) at 4s over the entire range). We find that the fraction of ALMA-detected galaxies in our z.=.1.5-10 samples increases steeply with stellar mass, with the detection fraction rising from 0% at 10(9.0) M-circle dot to 85(-18)(+9) % at >10(10) M-circle dot. Moreover, on stacking all 1253 low-mass (10(9.5) M-circle dot and an SMC-like relation at lower masses. Using stellar mass and beta measurements for z similar to 2 galaxies over the Cosmic Assembly Near-infrared Deep Extragalactic Legacy Survey, we derive a new empirical relation between beta and stellar mass and then use this correlation to show that our IRX-beta and IRX-stellar mass relations are consistent with each other. We then use these constraints to express the IRX as a bivariate function of beta and stellar mass. Finally, we present updated estimates of star formation rate density determinations at z > 3, leveraging present improvements in the measured IRX and recent probes of ultraluminous far-IR galaxies at z > 2.