What do we call an acting role that has very few lines?

The term used to describe an acting role that has very few lines is indeed a "bit part." A bit part usually refers to a small role in a play or film where the character has minimal dialogue and is often there to support the main actors or to fill out a scene. These roles can be significant in establishing the setting or context, even if the character does not contribute much in terms of spoken lines.

Supporting roles, although they may still be minor, typically involve more substantial interaction or lines, while lead roles generally dominate the narrative with considerable dialogue and development. Minor characters, similar to bit parts, also have limited presence, but they might sometimes have more lines than a typical bit part. Ultimately, "bit part" perfectly encapsulates the concept of having very few lines within a performance.