We are planning to connect to azure servicebus and blob storage from multiple sites. Is it possible to connect to them through a VPN instead of directly over the Internet to improve the security of the connection?
If it's possible can anyone advise how?
Yes, without know what kind of VPN you want/ what your networking set up is, I would suggest this:
https://azure.microsoft.com/documentation/articles/vpn-gateway-site-to-site-create/
Just put a machine on the azure network and send whatever bus data you want. You could even set up a proxy machine through that VPN if you are worried about publicly routed traffic.
Assuming they are in the same geo-location, any machine that is on the azure network that makes a request to blob storage or a service bus will never go through the internet. It will still use the public domain name but it will be sent through the azure networking fabric.
Without knowing the structure of what you're looking for, I would say the easiest way would be to set up an azure vm in the same geo-location.
This all being said, all traffic going to and from azure storage and service buses is encrypted and pretty safe.
Hope this helps.