When a pair of headphones are connected to an iPhone (whether wired or wireless), it's normal for the ring to be played both on the iPhone, as well as in the connected headphones. This is by design.
If you are not hearing the ringtone play via your Bluetooth headphones, make sure they are connected (not just paired) to your iPhone when you receive the call.
If you wish your iPhone to not ring when around people, and want the ringtone to play just via the Bluetooth headphones:
Make sure your iPhone is set to silent mode by using the Ring/Silent switch on the left side of your iPhone.
Make sure your Bluetooth headphones are connected to your iPhone. To ensure if the headphones are indeed connected, go to Settings app → Bluetooth, and check if your headphone listed under My Devices shows Connected in front of it. If it shows Not Connected instead, turn on your Bluetooth headphones and tap on it's entry here on your iPhone.
From the Apple Support document:
Put your iPhone in Ring/Silent mode
When your iPhone is set to ring, ringtones, alerts, and sounds play through your iPhone speakers.
When your iPhone is set to silent, you won't hear ringtones or alerts, but other sounds will play through your iPhone speakers and your iPhone will vibrate.
These settings affect only your iPhone speaker. If you use a headset, sounds play through your headset, even if your iPhone is on silent.