I found just the opposite to be true--that the big rush for slots was for the first year of infantil (at 3 years of age). Lots of people get turned away from their first choice (if it's a popular school). The following years (4 and 5 of infantil), it was much easier to get a slot due to attrition.
Really! That's interesting and GOOD! So there you have it, obviously what I said is not true across the board, and it's something worth researching when looking for your kid's school.
At the school I work at (a concertado), though, if you don't get accepted in the first year of Infantil you can all but forget it later on. And I know it's like that for many other concertados. But as MadridMadridMadrid pointed out, that doesn't have to be the case.
Chica, the money issue is very important when it comes to private schools...especially when you don't have it!
There's a bit of everything out there these days in the private school sector, so you really have to choose well.
The bilingual public school project could be a great choice. I haven't been following that subject too much so I don't know how it's going, whether it has expanded to other schools, etc. Does anyone know? (And yes, I will keep my fingers crossed)
And you always have the concertados, which used to be private, but now are tuition free. Most aren't bilingual, as far as I know.
But ultimately, if you speak enough English at home, personally I wouldn't be too worried about finding bilingual education, unless you'd prefer it for other reasons which is quite possible. My daughters' school (actually it's the same as mine) has four hours of English a week in Primaria, but I always speak to them in English, and they are pretty much bilingual now.