For a cover to use on the Bulldog Powered Drive Trailer Jack # BD500199 referenced in your question, I recommend the Ultra-Fab Protective Cover for Electric A-Frame Jacks # UF38-944020. This will easily slip over the jack and can be secured using the drawstring. This cover measures 12 inches x 14-1/2 inches. I have attached a video demonstration of the cover for you to check out.
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Quickly and easily install a 4-way trailer connector on your vehicle with this custom harness. T-One connector plugs directly into existing wiring - no cutting, splicing or tapping required. Powered to temporarily remove all floor coverings and cargo trays. Once you've plugged in the connector, you will have to route the harness through the jack storage compartment to the center of your vehicle. Before
Quickly and easily install a 4-way trailer connector on your vehicle with this custom harness. T-One connector plugs directly into OEM tow package wiring harness - no cutting or splicing required. Powered ModuLite reduces strain on wiring system. vehicle's wiring matches that of your trailer Powered module connects directly to avoid overloading your vehicle's electrical system Constructed of 16-gauge bonded wire Comes with dust cap for 4-way flat

This electric A-frame jack offers 22" of total travel and features an LED courtesy light for simple nighttime operation. Crank included for manual override in case of power failure. Features: Tongue jack positions quickly and easily with integrated drop leg Powered drive provides quiet operation and efficient use of electrical power No more hand cranking Easy-to-access on/off
The sealed, maintenance-free, 12V motor on this electric jack maintains high speeds, even with heavy loads. Extra-large, articulating footplate prevents sinking. Remote control has a 10' long Features: Electric landing gear jack lets you quickly and easily level and stabilize your trailer when used as part of a set Single-speed, 12V DC motor maintains a high speed, even with heavy loads
The Ultra-Fab Protective Cover for Electric A-Frame Jacks - Vinyl - 12" x 14-1/2" # UF38-944020 is the protective cover I recommend for your Husky Brute 4,500 lb Trailer Jack # HT87247. I've attached a photo of the dimensions when laid flat, but I've also attached a video to assist with the fit. It has a durable vinyl construction with integrated draw string closure.
The shipping weight of etrailer's Electric A-Frame Jack w/Footplate, # EJ-3520-BBX, is 25 pounds. This jack has received great reviews from our customers stating that it is well made easy to install. We don't put our name on just anything, so you can rest assured that this jack is good quality at a fair price. To protect your jack from the elements when not in use, I recommend the Ultra-Fab Protective Cover, # UF38-944020. 

The Camco Electric Tongue Jack Cover helps protect your electric tongue jack when it is not in use and in storage. The durable 3-layer spunbond polypropylene provides protection from harmful UV rays, excess moisture and dirt and debris. Tongue Jack Cover accommodates most styles and brands of Electric Tongue Jacks, and measures 18" tall x 7.5" wide x 8.5" deep.
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