This sample uses the Monkey.Robotics component in a Xamarin.Forms app to connect using Bluetooth LE to a Heart Rate Monitor (tested with the Polar H7) from both iOS and Android devices.
The Xamarin.Forms common code has a direct assembly reference to Robotics.Mobile.Core.dll in the Components directory, because components cannot be added to PCL projects.
The Monkey.Robotics component (and this app!) is in 'beta' and is provided to learn about using Bluetooth LE with Xamarin.Forms.
You can buy a Bluetooth LE compatible monitor like the Polar H7 from Polar direct or on Amazon for about $20 less.
The component that contains the Bluetooth LE abstraction for Xamarin.Forms is open-source, and is available on github. As noted on the component page it is still in beta.