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

Americans pronounce bouldering as BOHL-der-uhng (/ˈboʊldərɪŋ/). The L in "bouldering" is a dark L — the back of the tongue rises toward the soft palate, adding a small "uh" quality before the L. This is called the Dark L vs Light L, and it's one of the defining features of casual American English. It comes out as BOHL·der·uhng. Stress falls on the first syllable — keep everything else short and quick. You'll hear it in sentences like "He enjoys rock climbing and bouldering at the local gym".
Record yourself saying "bouldering" and play it back. The mic stays on your device — nothing's uploaded.
3 syllables, 7 sounds. Tap a syllable to jump to its row, then explore each sound's mouth shape and how it's made.
Press your lips together, add vocal cord vibration, then release.

Start with your mouth slightly open, then close your jaw slightly as your lips round. Shift your tongue back slightly, then stretch the back up.
Keep the tongue tip down and pull the back of the tongue up toward the throat. The 'dark' sound comes from the back.

The textbook way isn't wrong — it's just not how anyone actually says it.
The L in "bouldering" is a dark L — the back of the tongue rises toward the soft palate, adding a small "uh" quality before the L. Dark L adds a small schwa-like "uh" before the L. The back of the tongue lifts toward the soft palate.
Stress falls on the first syllable, not the others. Stretch BOHL — keep everything else short and quick.
Don't pronounce the second syllable too fully. The unstressed syllable reduces to a schwa — the lazy "uh" sound — in casual speech.
Americans use a relaxed retroflex R — the tongue curls back rather than rolling. The R is one continuous sound with the vowel before it, not two separate sounds.