Yes its possible if its with windows mobile phone or pocket pc with bluetooth. You need a bluetooth enabled computer and mobile phone. For dev you need to download the windows mobile 6 sdk.
Then developing of the communication between desktop app and mobile phone app, you can use the 32feet.Net is open source.
When you download it and installs (well it unpacks to program files folder) you will have the dll that you make reference to in Visual Studio. Also you will get some sample apps. One of them is a Bluetooth Chat that works in Desktop, Pocket PC and SmartPhone.