Another one of the three mountains of Moria, Bundushathûr translates as “Cloudyhead”. Tolkien gives a more literal translation, found on
Parma Eldalamberon XVII, pg 36.  It says there:

Since the basic D. name is Shathûr this element probably refers to cloud: it is prob. a plural = "clouds".  Bund(u) must therefore mean 'head' or something similar.  Possibly bund (BND) -u-shathûr "head in/of clouds".

Starting from that basis, bund(u) means "head".  The form bundu is similar to that of gundu in Felak-gundu, which is probably an "objective genitive", similar to what is seen in Adunaic.  If so, then bundu would be an accusative case form, and in composition state since it is the first element of the compound.  To an extent, this makes sense.  The radicals Sh-Th-R could be a verbal root meaning "to cloud, veil, or obscure".  The word shathûr "clouds" would then literally be "a thing that clouds/veils/obscures something", in this instance that being the head of the mountain.  However, it doesn't seem that an objective genitive would yield any different translation here from a standard genitive.  "Head in/of clouds" isn't much, if at all, different from "Head affected (veiled/obscured) by clouds".   The word order is different from the other objective genitives we see in Khuzdul: Felak-gundu "Hewer of Cave(s)" and Uzbad Khazad-dûmu "Lord of/to Moria".  I don't think then that this is the formal glossing, although it's an interesting coincidence.

The real question is where the -u- comes from.  On Ardalambion, Helge Fauskanger says:

...given that u is clearly a Dwarvish element meaning "of" (Bund-u-shathûr "Head in/of Clouds", TI:174), is it incorporated in baruk...

He goes on to suggest that this might be how the genitive/construct is formed for the declension of Khuzd and Khazâd.  I think I have shown in the portion about Baruk Khazâd! that this is probably not the case.  In Helge's defense, the information about bark being singular "axe", found in
Parma Eldalamberon XVII was not available when he wrote this (around 1999 or 2000).  Still, I have seen Ardalambion's Khuzdul article cited by enthusiastic Dwarf fans as near gospel, which is not surprising given Helge's rather thorough survey of Tolkien's languages and lack of much else.  Many people assume then that -u- is indeed an element meaning "of", especially when they see it tacked on the end of words in Khazad-dûmu and Felak-gundu.  If -u is indeed affixed to bund, gund, and Khazad-dûm, it would contradict the similarities of those examples to the Adunaic genitive and also with the -u ending found in mênu.  I think, then, that this is not a correct interpretation.

Tolkien gave the gloss
"possibly bund (BND) -u-shathûr 'head in/of clouds' ".  I have not seen anywhere where he suggests that -u- is either a genitive affix in bundu or a prefixed preposition in u-shathûr.  Instead, there is a much simpler explanation.  As a construct phrase, bund shathûr would mean "head in/of clouds".  In the construct of Semitic language, sometimes the English translation can be a little hazy.  Using the prepositions "of", "in", "at", "to", or "for" are not unusual.  When the words are conjoined into a compound, note that there would be a consonant cluster -ndsh- in the middle, which Khuzdul probably does not permit (or many other Semitic langauges).  That cluster has to be broken up, so the vowel -u- is inserted in between them, which is known as an "epenthetic vowel".  A -u- might be inserted simply because that was the previous vowel.

Given all this, bund is most probably "head" and singular, nominative, composition.

Shathûr then is "clouds". As I noted in the section on Baruk Khazâd!, if this follows the same declension as baruk, the singular would be shathr. I don't think it that's true, again because of final consonant cluster of -thr and that baruk is the indefinite form, not barûk.  Looking for some other explanation, CaCûC is a template vocalization seen in Arabic singulars, but the translation from Khuzdul is "clouds". I can easily see "clouds" as being a collective since they are usually found in multiples.  As it turns out, the word(s) for "cloud(s)" in Arabic uses a collective/singulative structure, so it's not out of line for Khuzdul to do so.  If CaCûC is a singular and/or collective pattern for Khuzdul, that would distinguish it a bit from the CaCuC pattern seen in baruk.  It's not something required, as both CaCûC and CaCuC are singular patterns in Arabic.  However, so far Khuzdul's templates seem to be slightly different from Arabic.  In Khuzdul, CaCuC is apparently a plural pattern instead of singular like it is in Arabic.  So, I will go out on a bit of a limb and suggest that shathûr is actually a collective, which wouldn't change the translation, but isn't stated by Tolkien either.  It is, however, the second element of the compound and very likely to be nominative and indefinite.

I thus view shathûr as "clouds" and collective, nominative, indefinite.

Bundushathûr is therefore a construct compound word, with a noun-noun word order.  The -u- between bund and shathûr is an epenthetic vowel and probably a schwa, so we could write the word as Bundüshathûr.

The Lord of the Rings, The Fellowship of the Ring, Book II, ch 3
The Treason of Isengard, pg 174, 432
Parma Eldalamberon XVII: Words, Phrases and Passages, pg 35, 36