I'm not sure what you've set up, can you explain a bit more? I've got Calibre set up to get a couple of its news feed daily, and send them to my Kindle via the free.kindle.com address (which is delivered via wifi only).
I take it you've got a 3G version?
You could still use the email address but use the "free" version: kindleusername>@free.kindle.com so it will only use the wifi network to send the news feed.
I have the 3g version, and so have not bothered to connect to wifi network since it's fairly complex due to my circumstances (away from home normally).
So I initially setup Calibre download the feed each day, and I attached my Kindle via USB and used the save to directory option to save the file to the Kindle.
Looking at your 2 answers and a quick Google, I think I should be using wifi for what I want to do. Just to check my understanding:
1. Calibre automatically downloads the feed to my computer
2. Calibre automatically emails this to @free.kindle.com
3. Amazon sends this across the Internet
4. Since my Kindle will be connected to the Internet it will receive the file(s) automatically
If correct, my sticking point was not making the leap and realising that when connected via wifi I would be also be connected to the Internet. So I was imagining some process where the file would have to be manually sent across my the wifi network from computer to Kindle!