I do not know what people mean when they talk about being washed in the blood.
The concept is wholly scriptural, here are some NT references for you. Jesus is the Lamb of God. He is a fulfillment of the passover lamb....
The next day John seeth Jesus coming unto him, and saith,
Behold the Lamb of God, which taketh away the sin of the world. (John 1:29)
Purge out therefore the old leaven, that ye may be a new lump, as ye are unleavened. For even
Christ our passover is sacrificed for us: (1 Cor. 5:7)
Much more then, being now
justified by his blood, we shall be saved from wrath through him. (Romans 5:9)
Having therefore, brethren, boldness to enter into the holiest
by the blood of Jesus, By a new and living way,
which he hath consecrated for us, through the veil, that is to say, his flesh; (Hebrews 10:19-20)
Elect according to the foreknowledge of God the Father, through sanctification of the Spirit,
unto obedience and sprinkling of the blood of Jesus Christ: Grace unto you, and peace, be multiplied. (1 Peter 1:2)
But if we walk in the light, as he is in the light, we have fellowship one with another,
and the blood of Jesus Christ his Son cleanseth us from all sin. (1 John 1:7)
And from Jesus Christ,
who is the faithful witness,
and the first begotten of the dead, and the prince of the kings of the earth. Unto him that loved us, and
washed us from our sins in his own blood, (Rev. 1:5)
And I said unto him, Sir, thou knowest. And he said to me, These are they which came out of great tribulation, and
have washed their robes, and made them white in the blood of the Lamb. (Rev. 7:14)
And they overcame him
by the blood of the Lamb, and by the word of their testimony; and they loved not their lives unto the death. (Rev. 12:11)