Everything is in the question title : Does Bpipe support Docker/Singularity container technology or Conda environments ?
I have not seen anything about in it the documentation or in Q/A so I'm unsure about it. There is a paper about Nextflow (Di Tommaso, P., Chatzou, M., Floden, E. W., Barja, P. P., Palumbo, E., & Notredame, C. (2017).
Nextflow enables reproducible computational workflows. Nature Biotechnology, 35(4), 316–319.
doi:10.1038/nbt.3820) assuming that Bpipe does not support Docker containers but since I have seen that Bpipe does now support AWS and GCS cloud computing and storage, I've thought that the information about Docker may be out to date.