I always read the line as a wake-up call, about the inevitability of death. Also, there is a sense that "sending to know for whom the bell tolls" is a separation of sorts. It's happening to him, and to her, but never to me.
I'm glad to hear you say the line is clumsy -- it is, and curious in light of his structure in other poems. Then again, he never quite reached 'organic', to my eye.
He is considered one of the early "metaphysical poets", but that description is also misleading, for when I read his stuff, I'm not left with that sense of oneness I should be experiencing. He's as dry as a bone - long on intellect, short on passion. This is probably the one poem by him I can tolerate.
A great image, that tolling bell. I thought it would be a good addition here, being a classic and all.