For a 3 week tour or less, depending where your rent from, it is usually not worth shipping your bike over and back again. Take possible damage and the hassles into account, and you'll want to rent for stays under 4 weeks.

Rental rates seem to depend on which country you will be renting in. For example Admo lists R1200 GS availability in Spain and Italy, but the rental in Italy is €345 more per week. That is serious coin on top of already silly rental rates.

Having toured Europe the last 14 years in a row, I know a bit about the area and riding there, so I put together an info thread...

Alps Motorcycle Tours - Priced Right