You can spray the TFR onto guttering by using a garden spray container. Fit a connection on the end of it that will fit your pole, put an on/off tap on your pole. Ensure the tap is off, connect your extended pole, pump the garden spray container up with pressure. Put your pole in place against the guttering, turn the tap on and away you go until the pressure drops, then it's a case of turn the pole tap off and re-pump the pressure back up on the garden sprayer.
No need for a pressure washer or a bucket, dipping the brush in it every couple of minutes.
Very simple really. A garden sprayer connected up this way will easily clean guttering at 30ft.