ŋaˈbʊːʔmɛ

The ? in IPA is the glottal stop
listen:
https://upload.wikimedia.org/wikipedia/commons/4/4d/Glottal_stop.ogg

The glottal stop is written with the letter h in the Bininj Kunwok alphabet. Remember this is nothing like the aspirated sound of h in English but rather a sudden stop in the airflow as in English oʼoh ʼsomething has gone wrongʼ or the Cockney deletion of t and replacement with a glottal stop as in what > wɒʔ

The ʊ vowel in bʊːʔ is lengthened somewhat.

nga- is the 'I' or first person singular prefix that goes on verbs.
-buhme is the verb 'to blow the didjeridu' in the non-past tenses (present and future).

The word is probably onomatopoeic 'buh' being the sound of the didjeridu. There is a related verb -buhmikan' which means 'to sing and be accompanied by the didjeridu'. The didjeridu in western Arnhem Land is not a solo or feature instrument as it has become in its popular contemporary incarnations elsewhere. Generally, the didjeridu in Arnhem Land music is used as an instrument of accompaniment for singing.

Na-ngale ka-buhme?
Who is going to play the didjeridu?

Bu nga-yawurrinjni minj nga-buhmeninj mako.
When I was a young man I didn't play the didjeridu.

Ma, yi-buhmen!
OK, start playing the didj!

Ka-mak kan-buhmikan?
Can you accompany me on the didjeridu (as I sing).