Hi Matu, I saw your post and created an account so that I could reply to it. I just returned from the Montana
Sepp Holzer workshop and I asked him a very similar question in regards to invasive weeds. When he heard the word "weeds" he answered that there was no such thing as a weed and that these so called weeds are doing their job and that
the answer is to change the environment where those plants thrive so that you can grow your food plants. He said that planting jerusalem artichokes or other tall fast growing food plants will shade out many "weeds". I have to say that while this is a wise answer the truth is that the three plants you mention - asian honeysuckle, bittersweet and bindweed - are very invasive and can shade out and kill
trees and smother food plants! They would love to climb a jerusalem artichoke. You already know this. I suggest either building your hugel bed to an area that is free of these plants or deal with them before building your bed because if you don't you will create a new unpaid full time job for yourself. All of these plants are runners and so you can deal with them by covering the ground with a heavy mulching of
cardboard (or set some plywood down) and then wait a couple of months (at least). Make sure you do this during the growing season... remove the
mulch or plywood and you can access and remove the vines asthey will rise to the surface. You will never get all of them so I recommend doing this several times over the span of at least a year to get it all out. If anyone has less time consuming recommendations I would love to hear them.