Pairing macbook pro to apple tv using bluetooth

Your TV & Mac should be on the same Wi-Fi network.

Are you also using the same Apple account?

Stream content using Home Sharing

You can stream music, movies, TV shows, photos, and other iTunes content from a computer or iOS device to your Apple TV. Both the device and Apple TV must be configured to use the same iTunes account.

Configure a computer. In iTunes, go to File > Home Sharing and choose Turn on Home Sharing. Enter your Apple ID and password, then click Turn on Home Sharing.

Note: In Windows 7 and Windows 8, iTunes menus are hidden by default. To show them temporarily, press the Alt key.

Configure an iOS device. Go to Settings > Videos or Settings > Music and turn on Home Sharing. Enter your Apple ID and password.

If you set up Apple TV and multiple devices with the same Apple ID, content from all the devices is available on your Apple TV.

Configure Apple TV. On Apple TV, in Settings , go to Accounts > Home Sharing. Turn On Home Sharing, then enter your Apple ID and password.

Stream content on Apple TV. Once you’ve configured all your devices using the same Apple ID, highlight Computers on the Apple TV Home screen and press the Touch surface. Libraries from your shared devices appear, and you can view or play any content from any library.

Use you Wi-Fi connection and turn on iTunes home sharing, I don't think you can pair your computer using BT.

You may want to connect a Bluetooth device to your Apple TV—such as an MFi-certified (made for iPhone, iPod touch, and iPad) game controller, Bluetooth headphones, or other accessories.