I have never tried to run it out of a bucket, but I have tried the same model of Karcher that you are using. There were times were it would not shoot water out even when hooked up to a 90 gallon tank. I figured out a trick and stuck it to the hose for a bit and let it build pressure. Its a messy task when you remove the hose but it might work.
1. Find a faucet and hook up the pressure washer. Make sure the pressure washer hose and wand are attached.
2. Run the pressure washer for a bit and then let it stop running with its auto stop feature. It should now have built pressure from the pump to the wand. Turn unit off and unplug, but do not release pressure on the wand.
3. Now the messy part is unhooking the hose connection. Turn it off to reduce backspray. And dont release the built up pressure from the wand.
4.) Hook up the hose accesorry and stick it in your bucket of water, Plug it in and release the pressure from the wand, it should now be sucking water from the tank. Hopefully this does the trick, as I have done this to my newer units before they were able to fully pump water from a detail tank. I did not find this problem with the newer X series Karcher untis though.
Hope these instructions make sense and let me know if it worked for you or not.