I don't quite understand what you're trying to say here:
I subsequently placed a negative BB entry which to date has been ignored by the outsourcer so as not to damage their online profile.
BB entries (whether positive or negative) do not require any acknowledgement or other action from the outsourcer concerned; in the interest of avoiding misunderstandings as to how the BB works, can you please explain what exactly you mean?
I would like to take this up with a moderator who can ensure that the entry is indeed posted and that other suppliers can reap the benefit of my experience with this particular outsourcer.
Well, I'd suggest contacting a Jobs/BB moderator, so we can look into it (which is a bit difficult in the forum).