Depending on the duration of your trip, it could be worth to at least find out about the costs of shipping your own bike. For reference, in Apr 2008, I shipped from Sydney to Helsinki by sea one DL650, and payed something like 700 euros, and that includes the ridiculously high (almost 200 EUR!) port charges in Helsinki. The actual ocean freight was quite cheap. But it took around 2 months to arrive. And naturally you´d have to do the whole process again, when returning, and then you´d have the quarantine inspections and everything.... I think for just 1 month, maybe it is not the right option.
　
I don´t know about Italy, but in Germany used bikes are relatively cheap, and there´s a good selection, so buying should be an option, and I would think the paperwork side is do-able, too. Inside the EU you won´t even be stopped at most borders. What to do with it after the trip I dont know (and if you´ve only got 1 month, then remember you dont want to spend many days sorting these after your arrival, AND before your departure!!) Renting is possible, too, but that´ll cost you some serious money, unless you can find some older bike that someone wants to rent. Maybe in fact a buy/sellback option could be your best solution, if you can find a suitable seller?
　
Italy is probably my #1 favourite destination in Europe - I´ve been there almost every year since I started motorcycling. The last time was June 2010, when we went to Sicily with my girlfriend. The only real downside is, that Italy has become quite expensive, but the pros still outweigh the cons I think! And sorry I cannot think of any favourite destinations in the country right now, as there are just too many, scattered all over it! September should be a great time to go there, the big tourist crowds are gone, but it is still warm, and most accommodations will still be open.