Yes, it is possible for bulk density to decrease with soil depth. Such a trend can be observed in soils affected by intensive human activities where the surface soil horizon is more compacted than the subsurface horizons. Bulk density typically increases as soil depth increases. The subsurface layers are more compacted and have less pore space because they have less organic matter, less aggregation, and less root penetration than the surface layer.
Yes it increases with the increase of soil depth because soil compaction increased with increase in soil depth. See the papers publised by your lab seniors- Catena by Vijyeta et al 2018, Science of the Total Environment by Rachita et al, Acta Ecologica Sinica by Vibhut et al etc.