Well, if you use Bluetooth you're no longer using the DAC inside the DAP, so it's not "driving" the headphones in the sense that GP meant. That said, most DAPs support bluetooth these days, with trendy codecs like LDAC, aptX-HD, etc. However, eschewing the device DAC kinda wastes a lot of the money you spent on the DAP.
For Bluetooth usage a year or two ago I would have recommended the Shanling M0. All these devices have awful touchscreens and the M0 is no exception, but it's tiny, light, and has long battery life. Unfortunately, in this space the manufacturers tend to discontinue products in favor of new ones within a year.
Can it drive Bluetooth headphones? That's the only reason I no longer use my Xduoo X3.
If I had something similar (small, minimal screen, dual TF slots) that worked with Bluetooth, I'd use it all the time.