Barring some update where Nintendo actually allows us to connect our bluetooth headphones/earpods to our Switch (not sure if such a thing could be added or not, but I bet it could), we are not left with a way to do so at the moment out of the box, but there do exist 3.5mm to bluetooth transmitters that can accomplish this. However, these things for the most part have less than ideal form factors, either dangling from a cord that connects to the 3.5mm jack (meaning you might need velcro or the like applied to the back of your Switch to not have it constantly dangling), or if they're one flush piece, they most seem to have a long connection from the jack to the bulk of the device which would not look good jutting out of the Switch like that. I've seen people do hardware mods to build such a transmitter right into a 3DS and I wouldn't be surprised if such a mod could be done for the Switch as well, however if you have both systems and would like to connect your bluetooth headphones to either interchangeably, you likely wouldn't want to pay to mod both systems just for the feature.
With all those things in mind, I believe I tracked down what may be the best solution at this time (short of doing a hardware mod), to get the audio transmitted from my Switch or 3DS or whatever to my bluetooth headphones. Its small, it rests directly on top of the system, doesn't dangle thanks to any cords, and it looks pretty sleek to top it all off. Its the Kokkia iSplitter: https://www.amazon.com/KOKKIA-iSPLI...d=1507837348&sr=8-2&keywords=kokkia+isplitter at $60, its not the cheapest solution out there, but it looks fantastic, and has the added benefit of being able to connect to 2 bluetooth devices, which can be really ideal for a situation where you and your friend are playing in tabletop mode but can't have the volume on due to annoying people around you (like being on a trip on a plane, a situation me and my friend have coming up for a trip we have for Vegas later).
If you're curious, I also got myself that new Nyko portable dock too. Anyway, I've been playing around on my Switch with the bluetooth transmitter and it works like a charm and isn't obtrusive or distracting in how it looks, so I'm loving it and would highly recommend this model for anyone looking for such a thing. i did see the same version available in white for $5 less, but I thought a white version wouldn't look as good with the Switch as the black version.
With all those things in mind, I believe I tracked down what may be the best solution at this time (short of doing a hardware mod), to get the audio transmitted from my Switch or 3DS or whatever to my bluetooth headphones. Its small, it rests directly on top of the system, doesn't dangle thanks to any cords, and it looks pretty sleek to top it all off. Its the Kokkia iSplitter: https://www.amazon.com/KOKKIA-iSPLI...d=1507837348&sr=8-2&keywords=kokkia+isplitter at $60, its not the cheapest solution out there, but it looks fantastic, and has the added benefit of being able to connect to 2 bluetooth devices, which can be really ideal for a situation where you and your friend are playing in tabletop mode but can't have the volume on due to annoying people around you (like being on a trip on a plane, a situation me and my friend have coming up for a trip we have for Vegas later).
If you're curious, I also got myself that new Nyko portable dock too. Anyway, I've been playing around on my Switch with the bluetooth transmitter and it works like a charm and isn't obtrusive or distracting in how it looks, so I'm loving it and would highly recommend this model for anyone looking for such a thing. i did see the same version available in white for $5 less, but I thought a white version wouldn't look as good with the Switch as the black version.
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