Can't say that i've ever seen any places that rent out Racing Bicycles as most (what i've seen anyway) only rent out mountain bikes. Would it not be better taking your own bike with you as they are accepted by some airlines & on trains etc. Also (just a thought?) why not think about cycling down from Finland to Ibiza?
NB: Travelling down to Ibiza on the bicycle is not so daft as it seem's as i've met quite a few cycling enthusiasts on the Islands campsites who have done such a trip. One middle aged couple last year actually cycled from their home near Espoo which i think is near Helsinki? The journey if i remember correctly took them just over a week of gentle cycling down to the Barcelona ferry port.
Well, basically driving a bike from Finland to Spain is not that big of a deal if you want to ride it. I don't basically want to do that. The reason why I need a racing bike is that I started racing again and having a one week break from training is a bit too much. Basically if I would keep my one week trip as a recovery week, I should ride two or three times, about 6 - 8 hours in total. Of course I could do it on mountain bike but I would prefer a road bike.
Taking my own bike to Ibiza is a bit too risky because it costs about 4500 euros and if the lovely people of the airline decide to mishandle it and they brake it, I don't have a bike anymore. Sure, I would get money from the insurance but getting a new bike in the middle of the season is not an easy thing to do.