Heh, I’ve had a Bluetooth set of earbuds from JBL for about 2 years and they’ve been providing great sound (and are really convenient as I work like an auto electrician a lot of the time and I can leave my phone in the toolbox). A good alternative perhaps besides building a portable amplifier.
I bought a Bluetooth speaker a couple of months ago. Sounds great, but if I watch a video, the sound is lagging. I thought about to get Bluetooth headphones, but after that experience I think, I just stay with cables.
To ensure (kind of) that your BT speaker/headphones will be able to work with video, check they implement "AptX low latency".
However, as they mention in the video, there are lots of ways this could fail: application playback issue, BT transmitter issue (although anything from the last few years should be able to handle this properly) or receiver issue (the most likely cause in older or cheap speakers).
