Place the very tip of your tongue slightly between your teeth. Blow air gently around it without voicing.

Americans pronounce threadbare as THREHD-bair (/ˈθrɛdˌbɛr/). Stress falls on the first syllable — keep everything else short and quick. You'll hear it in sentences like "Her threadbare coat was not warm enough".
Record yourself saying "threadbare" and play it back. The mic stays on your device — nothing's uploaded.
2 syllables, 6 sounds. Tap a syllable to jump to its row, then explore each sound's mouth shape and how it's made.
Place the very tip of your tongue slightly between your teeth. Blow air gently around it without voicing.

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

Touch the tip of your tongue to the roof of your mouth just behind your teeth. Add vocal cord vibration as you release.

The textbook way isn't wrong — it's just not how anyone actually says it.
In "threadbare", the "b" is not released — the articulators get into position but hold without the burst of air. Air stops but there's no release burst — the articulators hold position.
Stress falls on the first syllable, not the others. Stretch THREHD — 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.