First, the "washing of regeneration" is baptism. Second, this is Apostle Paul talking to Bishop Titus about proper instruction of the laity (verses 1-3). What Paul is saying is, -- we were originally sinners just like the laity is today, but we were washed by the Holy Ghost ans so shall they.
Besides, is not necessary to repeat that the gift has an intermediary in the Church every time it is mentioned. The gift of the Holy Ghost is linked to baptism in enough verses for us to say that that is the ordinary way to receive it.
Then what happened at Pentecost, a mass baptism or was that just another of the church's exceptions?
Washing of regeneration has nothing to do with baptism unless you believe in the error of baptismal regeneration.