I have the Cyclops H4 3800 Lumen on my bike, which is basically the bulb you posted by a different name, and it fits perfectly.
H4 LED Headlight Bulb | Motorcycle Lights | Brightest h4 LED Bulbs
You will have to bend the retaining bracket on the stock housing in order to get it to clear the heat-sink, and it will be a decently tight fit to get the boot over it (some here have suggested to leave it off, I kept mine). Other than that it's perfect -- the little vent in the back of our bucket is even perfect, as it lines up perfectly with the fan output.
Definitely a worthwhile upgrade my bike headlight now has more output than most cars I see on the highway. Our bucket seems to put out a good beam pattern as well -- no holes, no blinding oncoming cars.