For a "proper" touring bike (whatever that is!
) I'd google specialist touring/expedition/adventure cycling shops and contact them directly. I know that some rent out bikes.
You'd also need to consider what gear you have, will bring with you and need locally. I'm thinking racks, panniers etc. Saddles and pedals too, perhaps.
Another option is to arrive on spec and buy a bike locally. If you're reasonably bike savvy you should be able to avoid a lemon and pick up something decent for a very reasonable price.
For instance I know of a guy here in NL who makes a tidy living selling barely used expedition bikes.
Similarly, Decathlon is a large, European chain store that sell & equip bikes. Buying a bike there would be relatively cheap with the comfort of being able to roll into another store somewhere else if there were any mechanical issues.
Sell (difficult) at the end or donate to a cycling charity when you're done. Mind you, I had a warmshowers guest once who flew into NL, bought a cheap second hand bike in a local bike shop, rode around the country and brought it back to the shop and got half her money back!
Finally, this could be a good opportunity to pick up a brand spanking new Touring/Expedition bike to your own specs that you pick up over here, tour on in Europe and ship home. I believe there's the possibility of getting a VAT (sales tax) refund back. Thorn (UK), Santos, Koga (NL) would be some of the big touring bike manufacturers.
But.... probably the most important factor in a touring bike is that it is comfortable! That's difficult to organise in advance so whatever option you go for I'd plan on doing a shortish circular route from where you pick up the bike to test it out and be able to have any adjustments or component changes made before heading off proper.
