Have hired in Spain where there is a good supply of hire bikes. One (
BikeIberia) will get the bike to you anywhere in Iberia (natch) then arrange collection at wherever you stop. Range of bikes
Have done the FIFO too, flying into Logrono in Spain and then popping into
Decathlon for a MTB for €300. Their bikes are fairly pedestrian but last. Met a guy who did the same but purchased the budget level one (€150). Did the job though. Also Decathlon now sell second life/second hand bikes.
The benefit of a Decathlon bike IMHO, is that wherever you take it in Europe there is a Decathlon with spares for it. Managed to pick up bits for that bike in both Italy and Greece when cycling through.
Or take your pride and joy with you and have baggage handlers mash it for you.