Install the following:
sudo apt-get install pi-bluetooth blueman
Make sure to reboot pi after this installation.
Now on your raspberry pi console, click on Bluetooth -> add your device and check by sending your files.
RPi 3B only has one antenna on board, so yes, it will be shared. Sharing is managed by the adapter firmware which is closed-source. Even if done right, it will not be as good as separate antennas.
You can get a USB dongle for either WiFi or BT (and use that instead of the built-in adapter) to get two separate antennas.