Bash is great, and interacting with webservices is fairly easy. Of course, to do that you will need to know whether the user is connected to the web.
So, to check the network connection in Bash I typically use a simple ping against the primary Google DNS server (8.8.8.8).
Text Snippet:
#!/usr/bin/env bash
PUNG=`ping 8.8.8.8 -c1 > /dev/null 2>&1`
if [ $? -eq 0 ]; then
echo "Looks like you're connected!"
else
echo "No connection."
fi
And that's it. Fairly easy to use, simple to understand, and quite reliable (from my experience).
If you have any suggestions, or comments, feel free to leave them below.