No matter how slowly you run a drill type mixer you will incorporate air.
Letting the bubbles rise to the top is not the answer IMO, it takes for ever and you often still end up with jars with a thin layer of froth on top. I used to use one of these Honey Creamers from Thornes which does an amazing job.
You use it like a potato masher but don't let the top come above the surface of the honey. It's hard work as you need to "work" the honey for 5 minutes or so on a regular basis for a couple of days before bottling...Working it regularly keeps breaking the crystal size down as they shear as they pass through the openings on the paddle..But it's hard work and monotonous...which is why I bought a machine that does the job for me.
In a few seconds there will be several posts saying you don't need to to do all of this....Suggest you try it with an ordinary potato masher and I suspect you will be very pleasantly surprised as to how velvety smooth the finished product is. I only make approx 700lbs of soft set honey a year so I obviously don't have a clue what I'm talking about