There is no formal relationship, so far as I know. Bioconductor is 'part of' bioconda in the sense that you can install things using bioconda, but not in any other way.
My experience with 'conda' like substances is that it can be really helpful for installing different python environments for various purposes, because otherwise python seems to be sort of a drag to deal with. R and Bioconductor aren't hard to deal with IMO, and layering something else on top seems to be less useful. Even without sudo privileges on linux it's simple enough to have your own version of R/Bioconductor, as long as you have the space in your personal directory or have read/write privileges elsewhere.
To me, bioconda is like a Mac. It makes it easy to do the things that the developers think you want to do, but you are limited to a certain extent by their vision. If you want to do something other than what they think you should want to do, it can be a pretty painful experience. This is why I don't use a Mac. I have done so in the past, but using R on a Mac isn't IMO very straightforward as compared to Linux or even Windows.
Anyway, if you are happy working within the confines of their vision, then it might be easier. But you may be limited by the package versions that they have available, etc, which won't be true if you just install R/Bioconductor conventionally.