I would definitely go with Web Sites, it would be a lot easier and it would fit your needs.
No service bus needed unless you want to reach a local network computer from your cloud served site (or other)
Edit: What you will host on the Azure Web Site will be a regular ASP.net app with WCF services, just as you would in your local server. If you need to consume WCF services, the other group needs to tell you their url, and you will have to do the same to provide services.