Hi LondonLady, sorry I can’t help with yr query but you could get the high speed train (AVE) to Valencia, or hire a car from Madrid & drive over. Last time I looked Ryanair were doing Madrid – Alc for 10e, about what the service is worth.
I have shipped bikes over to Spain separately, I live in Spain so can wait.
Where are you heading? I have done loads of biking between Benidorm & Denia (I use the local train alot to get to new places). It is hot & sunny at the moment so pack the sunlotion.
Anything else I can help with just ask, email in profile.