I shipped my 2004 Goldwing to Europe in the spring of 2018. I have been over three times since then to ride around Europe. I usually ride for a month and return home. Not sure where you live but you do have a couple good options. Shipping usually does involve a little preparation, such as leaving the gas tank very empty (but not completely) and disconnecting the battery.
I used Stefan Knopf Tours located in Heidelberg. In fact my '04 is still there. I paid $1,400 to ship it over. I rode from Conroe Texas to Orlando Florida about mid-March. The bike was in Heidelberg by the end of April. So, if you are wanting to ride some here, drop it off and have it be in Europe the next week, this isn't a good option. I have other bikes, including an '18 DCT Tour so sending my '04 over and leaving it, wasn't a big deal. Stefan also picks up in Huntington Beach California. Absolutely NO hassle. I dropped it off, handed Stefan a check and a little paperwork (including the Title) and I was done in about 15 minutes. I got to Frankfurt in June, rode the van to Heidelberg that Stefan arranged, the Wing was waiting for me at Stefan's place. So, here is breakdown of my costs in USD.
Pickup and Drop off: Huntington Beach,CA or Orlando, FL to Heidelberg, Germany
Shipping: $1,400 USD one way. So obviously $2,800 both ways.
Storage: first months through about June is free, after that it's about $440 a year
Insurance: about $220 a month, but you only need it when riding
Health Insurance (optional): $100 / month
Breakdown towing (optional): $120 / month
As others have mentioned Air Canada is also a good shipping option. It may be cheaper than Stefan, but they usually don't publish their shipping rates until April of the year you want to ship. And I understand that it isn't much of a hassle either. Although I have been told that you have to fly on the same flight as your bike. Your personal air fare will likely be more expensive than what you can get on other airlines. From other riders at Stefans B&B, I heard there are four places in Canada that they pick up. Like Victoria, Calgary, Toronto and may be someplace further east. And I believe they just go to Frankfurt. You will still need all the insurance and choose any other coverage options I mentioned above.
I found that shipping isn't as big a hassle as everyone says, but you do risk your own bike and damage in shipping and storage. Rental is also a choice although it will be more expensive if you stay longer than a couple weeks. I don't like riding in an organized tour, because you can't really ride your ride. Also, you will be limited on the bikes to rent and setting it up the way you like would be unlikely. But, it does eliminate all the guesswork. Buying a bike over there and selling it when your done is also an option, that is what my buddy did. But there are several issues you have to be comfortable with that option. You will be required to give a European address (obviously someone who is willing to let you use their address), unless you buy a US title bike. Plus, finding the RIGHT bike, then getting it set up the way you like it. But, buying then selling may be the cheapest option of all.
Someone mentioned maps. I use Garmin GPS's; a Zumo 595, two Zumo 665's, a 376c and a 378. I only take the two 665's to Europe. I had to do a little work but now have a complete map of Europe using OpenSourceMaps.NL, which is free. This works as well as any of the Garmin maps and also works with Basecamp and Mapsource. Setting it up is a little complicated, but not insurmountable with a little patience. I can help with this, but explaining it here would be too much.
Really, the hardest part to all this is making a decision. If you are of the persuasion that a couple thousand dollars one way or the other isn't a big deal, then any of these options are available.
There is some other stuff, but I tend to drag on with my explanations. And right now it is cutting into going for a ride.

I am taking my K1600 north, to get out of the hassle known as the Lone Star State Motorcycle Rally!