Dragon's Breath can still be bottled for as long as the entity persists. After each bottle, the hitbox reduces in size.

Expected Result
Once the size of the hitbox is reduced to zero, the entity will no longer be able to be bottled and/or the entity will disappear

Observed Result
Once the size of the hitbox becomes zero, it can still be bottled until the entity despawns, meaning it can be bottled for far longer then expected.

Attached is a video demonstrating the bug in a vanilla world.

Note - This happens most times but does not happen every time and from my testing, only works from the breath at the "bedrock fountain", not from the purple fireball things.