What L said wasn't a bluff. He was just repeating what he said just before Light and Misa were confined.
In chapter 32, he said
Light: Didn't you say that it's scary to appear in public? Is this really okay?
L: I realized that if Yagami-kun isn't the killer, I should be fine... Since only Yagami-kun knows who I am.
L: So if I die in the next few days...
L: Yagami-san will take over the investigation and every L will know that Yagami Light is the killer.
Yagami presumed this to be a bluff, that there were no other L around and called that bluff later by using Rem.
But we see later that this is exactly how it went down. The other L being Mello and Nero. N almost knew from the start the new L was the killer.
In chapter 33-36, Misa is confined. Light makes preparations for later and turns himself in. Both Misa and Light were confined for more than 13 days and are finally released again.
In chapter 37, L handcuffs Light, because at this point L still believes Light to be the killer. He just can't prove it due to their long confinement and the continuation of murders. So he still believes what he had said in chapter 32 and thus to repeat this in front of everybody he says that they will both share the same faith.
Later when L actually dies, Light can escape imprisonment, because of the fake rules he had put up. If the 13 day rule wouldn't have been in the Death Note he would have been captures by the NPA and L's prediction would have come true.