Buzundush was the original Khuzdul name for the Silverlode River, called Celebrant in Sindarin. At first, I hadn't intended to include it here because Tolkien discarded the name and replaced it with Zigil-nâd. That also was discarded and changed to Kibil-nâla. Buzundush was said to mean "Blackroot", and corresponded to the Sindarin name Morthond, which was "dark root". Eventually, the name was kept, but applied to an entirely different river: the one which flowed from the Paths of the Dead, through central Gondor. The Khuzdul name Buzundush is not mentioned at all in connection with the river once it was applied to the Morthond of Gondor. Even though Tolkien never "officially" provided a Khuzdul name for the Morthond River in Gondor, the fact that the same translation could apply and doesn't contradict any of our other information on Khuzdul means that we can go ahead and use these words.
Dush probably means "dark" or "darkness", especially if the root was imported into the Black Speech or Orkish in the compound word Dushgoi "Minas Morgul". The radicals would be D-Sh-', and follow the same or similar template as khuzd, khazâd. A geminated root (D-Sh-Sh) or a root with a weak middle radical (D-Y-Sh or D-W-Sh) would more likely yield a final form of dûsh. It's the second element of the compound, so is most likely to be nominative and indefinite.
I will say dush is "dark, darkness" and is singular, nominative, indefinite.
would be "root". If a "root" corresponds to the roots of trees, then
it would be easy to see this as a collective noun, since roots will
almost always be found in bunches. The form is the same seen in Tumunzahar, notably ending in -un. To my knowledge, nowhere does Tolkien state that the root of buzun (pardon the pun...) is B-Z-N. Therefore, we can then see the same suffix of specificity seen in Tumunzahar. The root would be B-Z-', B-Z-Z, B-Y-Z, or B-W-Z, providing us with the collective noun buz or bûz "roots". From there, both of those would have a composition form buz. Apply the -ûn suffix and we get the singulative form buzûn "root". That, in composition, is then also reduced to buzun.
My guess then is that buzun is "root" and is singulative, nominative, composition.
I should state for the record that the translations of the two elements could very well be reversed, leading to a different gloss. That said, Tumunzahar appears to follow a similar derivation that seems far more likely than not. Assuming that is true, my interpretation of Buzundush lines up well with that, and is perhaps slightly more likely due to the comparison with Dushgoi.
See the write-up on Tumunzahar for more information.
The Treason of Isengard, pg 166-167, 241