ザンブカ　would be the correct spelling. ム is "mu", and ン is the "n" you should have in place of it.
also, サ and ザ are different; without the particles it's "sa", and with them its "za".

Wonder, how did you come to write it this way? As someone who knows katakana and hiragana very well, I can assure you the above image is incorrect for "zanbuka". Instead it says "samubuka".

When I learned Japanese, I remembered that words can take on a different pronunciation but still retain their katakana(i.e. sakura and zakura still use 桜).

That's for kanji, when spelling out individual words with kata and hira, you definitely need to make sure you have the correct forms or else people won't know what you want to say.

And as a corollary, a lot of japanese kanji includes furigana (little hira/kata above kanji) to let people who don't know that kanji how to pronounce it.

But, I guess it's not a big issue seeing as not many japanese people visit these english websites :P