To connect a pair of Bluetooth headphones (including AirPods, Bose QC35 etc.) to Nintendo Switch, you'll need a USB Bluetooth adapter. The adapter can either be regular USB (use on dock) or USB Type-C... something like these:
Avantree C51 (Learn More)
Avantree DG60 (Learn More)
How to do it?
1. Plug the adapter into your Switch. If you're using a Type-C adapter, plug it directly into your Switch's Type-C port. If you're using a USB adapter, you'll plug it into a USB port on your Switch charging dock.
2. Get your Bluetooth gaming headsets or earbuds 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 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 C519M (Learn More)
Avantree DG59M (Learn More)
Check more USB Bluetooth adapter for PC & Gaming and Noise cancelling gaming headphones.
Here's a video that'll give you an idea about Headphone + Adapter Combo:
We understand that this is a rather complicated technology so please feel free to contact us at support@avantree.com if you have any questions, we'll do our best to help.