英语句子成分划分？

I happened on one occasion to be spending a few days there, waiting for a ship, and I was introduced to him at the British Club.里的waiting for a ship是属于什么成分，是插入语吗？

I happened on one occasion to be spending a few days there,waiting for a ship, and I was introduced to him at the British Club.

有一次我碰巧在那里呆几天，等一艘船，我在英国俱乐部认识了他。

这里非谓语动词结构waiting for a ship是伴随状语或者理解为目的状语也可以。