We report on growth of high quality BaBiO3 single crystals and their characterization via x-ray diffractometry (XRD), atomic force microscopy, surface nanoindentation, electronic transport, and magnetic susceptibility. The grown crystals are mildly twinned, which was analyzed and twin law with twinning factor is obtained. Surface studies revealed very peculiar adsorbate assisted and mechanically induced degradation. The XRD and induced surface degradation point to micro twinning with large strains on the twin boundaries. The observed as-grown surface morphology suggests high sensitivity of crystal growth to the growth temperature variations and might be related to twinning. Electronic transport and magnetization measurements are consistent with previous works, but systematic comparison of latter with earlier works renders an interesting question: can local moments be structurally induced in BaBiO3?