Tongue pulls back slightly from the D position, blending into R. Sounds close to 'jr'.

Americans pronounce dribbling as DRIH-bluhng (/ˈdrɪbləŋ/). In "dribbling", the "dr" cluster blends into a "jr" sound — a natural American English pronunciation. This is called the DR Sounds Like JR, a hallmark of natural-sounding American speech. It comes out as DRIH·bluhng. Stress falls on the first syllable — keep everything else short and quick. You'll hear it in sentences like "She practices dribbling the basketball to improve her control".
Record yourself saying "dribbling" and play it back. The mic stays on your device — nothing's uploaded.
2 syllables, 7 sounds. Tap a syllable to jump to its row, then explore each sound's mouth shape and how it's made.
Tongue pulls back slightly from the D position, blending into R. Sounds close to 'jr'.

Curl or bunch your tongue without letting the tip touch the roof of your mouth. Brace the sides of your tongue against your upper back teeth, and round your lips slightly.
Drop your jaw slightly with relaxed lips. Touch the tongue tip behind the bottom front teeth and arch the top-front toward the roof.

Press your lips together, add vocal cord vibration, then release.

Place the tip of your tongue against the alveolar ridge just behind your top front teeth, the same contact point as /t/, /d/, and /n/. The difference is what happens to the air: for /l/, you let it flow continuously around the <em>sides</em> of the tongue (that's why /l/ is called a lateral). Turn your voice on the whole time. Lips stay relaxed, no rounding or flaring. For the Dark L variant at the end of a syllable, also pull the back of the tongue up and back toward the soft palate.

Relax your lips, jaw, and tongue completely. Drop your jaw slightly and keep the tongue neutral.
Lift the back of your tongue to the soft palate. Lower your soft palate to let air flow through your nose.

The textbook way isn't wrong — it's just not how anyone actually says it.
In "dribbling", the "dr" cluster blends into a "jr" sound — a natural American English pronunciation. /d/ shifts toward /dʒ/ ("j"), so DR sounds like "jr".
Stress falls on the first syllable, not the others. Stretch DRIH — keep everything else short and quick.
Don't pronounce the first syllable too fully. The unstressed syllable reduces to a schwa — the lazy "uh" sound — in casual speech.