My experience has been that automating the track send works best for me. That way only the audio I choose has echo applied to it. 
 
I've tried the ducking method and found it to be okay, but it I am feeling particular, I will definitely go for track send automation.  

Having the delay on the buss which the vocal track outputs to is no different from having the delay as an insert effect on the track.
You might be better off running the send to it's own bus in a send/return configuration (especially if you want more than just one vocal track to be effected) and bring the delay up in parallel. Automate the bus volume to bring the effect in and out, or automate the send levels on individual tracks.

If you automate the buss volume, rather than the track send, you may get echos from any material present earlier in the track. This may not be what you desire. I often only wish for the final word, or even the final syllable to have echo applied to it. Using automation on the track send facilitates this for me. 

Yeah that can happen.
 
I quite often split a single word into it's own clip and process that

I have started understanding this slowly.... Thank you all for helping me...

See "Craig Anderton's - Tip Of The Week No.64". This shows 'gating' of a reverb on a vocal track. Just swap the reverb for a delay and you have what you're after. I think Craig's tips are great, and often find things there that are a genuine help in my everyday workflow.

Another resource that walks through the setup is this blog post by Dan Gonzalez. The end result is "We are creating a delay and reverb effect that only occurs when the vocalist is NOT singing," which seems to be your question in the OP.

!! METTELUS !!
Exactly shown in the blog what I wanted to do..
Thanks a ton to everyone giving me time and suggestion.

It was all Dan's doing, I just remembered reading it . That same principle works well for many different FX, just tailor the chain to what meets your needs.