To connect a pair of Bluetooth headphones (including AirPods, Bose QC35 etc.) to PlayStation 4, you'll need a USB Bluetooth adapter. The adapter can be plugged into the USB ports on your PS4. They look something like this:

Avantree DG80 (Learn More)

Avantree DG60 (Learn More)

How to do it?

1. Plug the adapter into the USB Port on your PlayStation 4. 

2. Get your Bluetooth Headphones into Bluetooth Pairing Mode. Please see your user manual if you're not sure how.

3. Get the Adapter into Bluetooth Pairing Mode as well.

4. Keep them close to each other. Once connected, you'll be good to go.

Here's a Video that'll give you an idea on how to do it:

Regarding the Audio Delay Issue

If your Headphone does not support aptX Low Latency or FastStream, you'll experience slight audio delay. If it really bothers you, the easiest solution is simply to go with a pair Bluetooth gaming headset that supports aptX Low Latency or FastStream.

You may also consider a pre-paired Headphone + Adapter set; these sets or "combos" come with built-in low latency technology and gives you much better Audio Quality when you'd like to do in-game voice chats. What's more, these sets usually still allow you to use the adapter and/or the headphone independently if you want... quite convenient. 

These Sets look something like this:

Avantree DG59M (Learn More)

Avantree DG59M (Learn More)

check more about noise cancelling gaming headphones

Here's a video that'll give you an idea about Headphone + Adapter Combo:

You may be interested in PS5 Bluetooth Headphones or Bluetooth headphones with mic for pc

We understand that this is a rather complicated technology so please feel free to contact us at support@avantree.com if you have any question, we'll do our best to help.