Front hitch and motorcycle questions

With my truck and camper, it would be nearly impossible to overload the front axle.
My max front axle weight is 5940lbs. With the camper loaded and the with the front hitch and carrier loaded with a 2000 watt generator, 5 gallons of gas and 6 gallons of water, the total front axle weight is 4550lbs, leaving me with another 1390lbs of additional front axle capacity.
With my long, heavy camper, the front axle is unloaded a little. I find the added weight from the front hitch aids the steering.

Is it diesel or gasoline motor?
With heavy diesel, putting 500lb in front can very easy overload your front axle, so you have to be carefull with the idea.
Even if big bike will not obstruct the front view.
I had front hitch on my Superduty and I don't think I would like to have 500lb bouncing on it. Did carry 200lb of generator and other stuff just fine.
For stuff of this weight you need triple receivers for additional support or other means of side support.

First, weigh the truck with the camper on board and see how close you are to axle weights. Rams are usually pretty close to the limits but in 2013 or 2014 the increased the front axle rating giving a bit more load capacity.

While a hitch may be rated for 500 pounds, that is for the weight only being less than 6" from the end of the hitch. The COG for the bike will need to be at least 18" from the hitch which reduces the capacity to about 300 pounds. So while it may be possible to carry a light motorcycle, I wouldn't want to carry one more than about 200 pounds.

An alternative would be to replace the two took hooks with snub receivers then build a custom rack using both points. This will greatly reduce the wobble and double the load capacity. However, I still would not want to carry a 400 pound bike, but a 300 pound bike would be within reason.

We carry two adult bicycles (est. 70 lbs.) on a front hitch and they bounce around like crazy. We use six bunge cords to dampen the bouncing.

On a bike rack using the two points and a single ratchet strap, I carry two bikes and the only movement is a bit of handle bar vibration. Trick is I have a solid point to pull the frames against and have a block of wood between the bikes so everything can be pulled tight together.

I'd vote for an enclosed trailer.
We carry two adult bicycles (est. 70 lbs.) on a front hitch and they bounce around like crazy. We use six bunge cords to dampen the bouncing. I can't imagine how much bouncing 500 lbs of cycle would occur.

What weight of bike?
Have you weighted your truck and know what the front axle has for carrying the bike.
With the rack and carrier I am ~ 370 lbs and have had no issues.