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

Americans pronounce barbell as BAR-behl (/ˈbɑrˌbɛl/). The L in "barbell" 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 why Americans sound more relaxed than the textbook. It comes out as BAR·BEHL. Stress falls on the first syllable — keep everything else short and quick. You'll hear it in sentences like "The barbell is used for heavy weightlifting exercises".
Record yourself saying "barbell" and play it back. The mic stays on your device — nothing's uploaded.
2 syllables, 5 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.

Drop your jaw moderately. Touch the tongue tip behind the bottom front teeth and lift the mid-front part slightly toward the roof.

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 "barbell" 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 BAR — keep everything else short and quick.
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.