Is it a Surface or Surface Pro? If it's a Surface Pro, there are several AirPlay receiver programs you can get hold of which will let you AirPlay cast from any iOS and play on your Spro screen. I'm not sure if you can get these for the Surface, however.
I recall you may also need to install iTunes to get the Bonjour protocol installed, which isn't great.
An alternative is to use something like Webex, TeamViewer or GotoMeeting, which may have versions for the Surface, but I suspect you'd be limited to seeing content at the screen resolution of the iOS device, and isn't something I've ever tried. These will be more of a faff to set up too.
