We present the improved constraints on couplings of solar axions and more generic bosonic dark matter particles using 737.1 kg days of data from the CDEX-1B experiment. The CDEX-1B experiment, located at the China Jinping Underground Laboratory, primarily aims at the direct detection of weakly interacting massive particles using a p-type point-contact germanium detector. We adopt the profile likelihood ratio method for analysis of data in the presence of backgrounds. An energy threshold of 160 eV was achieved, much better than the 475 eV of CDEX-1A with an exposure of 335.6 kg days. This significantly improves the sensitivity for the bosonic dark matter below 0.8 keV among germanium detectors. Limits are also placed on the coupling $g_{Ae}<2.48\times {10}^{-11}$ from Compton, bremsstrahlung, atomic-recombination, and deexcitation channels and $g_{AN}^{\mathrm{eff}}\times g_{Ae}<4.14\times {10}^{-17}$ from a ${}^{57}\mathrm{Fe}$ M1 transition at 90% confidence level.