NOTE: The following Scriptures are from the Young's Literal Translation YLT Bible.

There are multiple women preachers in the Bible, such as Phebe, Priscilla, Junia, Deborah, Lydia, Anna, and more.  However, many seem to forget the preaching of a Samaritan woman, which helped lead many to Christ:

 John 4:1-42

1 When therefore the Lord knew that the Pharisees heard that Jesus more disciples doth make and baptize than John,

² (though indeed Jesus himself was not baptizing, but his disciples,)

³ he left Judea and went away again to Galilee,

⁴ and it was behoving him to go through Samaria.

Jesus went to Samaria.  The Samaritans were considered 'dogs' and 'half-breeds' by the devout Jews, and Jews would have nothing to do with Samaritans, yet Jesus specifically went to Samaria.

⁵ He cometh, therefore, to a city of Samaria, called Sychar, near to the place that Jacob gave to Joseph his son;

⁶ and there was there a well of Jacob. Jesus therefore having been weary from the journeying, was sitting thus on the well; it was as it were the sixth hour;

 This was noon.  The sixth hour was noon.

⁷ there cometh a woman out of Samaria to draw water. Jesus saith to her, `Give me to drink;'

Jews weren't supposed to speak with, or have anything to do with Samaritans, yet Jesus purposely went to Samaria, stopped at a well in Samaria, and spoke to a Samaritan woman.

⁸ for his disciples were gone away to the city, that they may buy victuals;

⁹ the Samaritan woman therefore saith to him, `How dost thou, being a Jew, ask drink from me, being a Samaritan woman?' for Jews have no dealing with Samaritans.

¹⁰ Jesus answered and said to her, `If thou hadst known the gift of God, and who it is who is saying to thee, Give me to drink, thou wouldest have asked him, and he would have given thee living water.'

Jesus doesn't even address the issue of him being a Jew, addressing a Samaritan woman.  Instead, He goes to what actually does matter, and what is actually important.

¹¹ The woman saith to him, `Sir, thou hast not even a vessel to draw with, and the well is deep; whence, then, hast thou the living water?

¹² Art thou greater than our father Jacob, who did give us the well, and himself out of it did drink, and his sons, and his cattle?'

¹³ Jesus answered and said to her, `Every one who is drinking of this water shall thirst again;

¹⁴ but whoever may drink of the water that I will give him, may not thirst -- to the age; and the water that I will give him shall become in him a well of water, springing up to life age-during.'

¹⁵ The woman saith unto him, `Sir, give me this water, that I may not thirst, nor come hither to draw.'

¹⁶ Jesus saith to her, `Go, call thy husband, and come hither;'

¹⁷ the woman answered and said, `I have not a husband.' Jesus saith to her, `Well didst thou say -- A husband I have not;

¹⁸ for five husbands thou hast had, and, now, he whom thou hast is not thy husband; this hast thou said truly.'

¹⁹ The woman saith to him, `Sir, I perceive that thou art a prophet;

²⁰ our fathers in this mountain did worship, and ye -- ye say that in Jerusalem is the place where it behoveth to worship.'

²¹ Jesus saith to her, `Woman, believe me, that there doth come an hour, when neither in this mountain, nor in Jerusalem, shall ye worship the Father;

²² ye worship what ye have not known; we worship what we have known, because the salvation is of the Jews;

²³ but, there cometh an hour, and it now is, when the true worshippers will worship the Father in spirit and truth, for the Father also doth seek such to worship him;

²⁴ God [is] a Spirit, and those worshipping Him, in spirit and truth it doth behove to worship.'

Jesus here defines that the true worshippers of God are those who worship him in spirit and in truth.  There is no gender differential given here, nor any differential in race or societal status. Truth in Christ is what's paramount, not social standing, race, or gender:

"Jesus saith to him, `I am the way, and the truth, and the life, no one doth come unto the Father, if not through me;"  -John 14:6

"for as many as to Christ were baptized did put on Christ; there is not here Jew or Greek, there is not here servant nor freeman, there is not here male and female, for all ye are one in Christ Jesus;"  -Galatians 3:27-28

²⁵ The woman saith to him, `I have known that Messiah doth come, who is called Christ, when that one may come, he will tell us all things;'

²⁶ Jesus saith to her, `I am [he], who am speaking to thee.'

²⁷ And upon this came his disciples, and were wondering that with a woman he was speaking, no one, however, said, `What seekest thou?' or `Why speakest thou with her?'

Upon the disciples seeing Jesus speaking with the Samaritan woman, they seemed surprised that Jesus was speaking with a woman.  The Woman, apparently unphased by the male disciples' shock at her gender, went into the city to preach to the men there, as we see below:

²⁸ The woman then left her water-jug, and went away to the city, and saith to the men,

²⁹ `Come, see a man, who told me all things -- as many as I did; is this the Christ?'

³⁰ They went forth therefore out of the city, and were coming unto him.

The men of the city listened to the woman, and decided to go to Jesus themselves, and see if He was indeed the Messiah/Christ.

³¹ And in the meanwhile his disciples were asking him, saying, `Rabbi, eat;'

³² and he said to them, `I have food to eat that ye have not known.'

³³ The disciples then said one to another, `Did any one bring him anything to eat?'

³⁴ Jesus saith to them, `My food is, that I may do the will of Him who sent me, and may finish His work;

It was the will of God the Father that Jesus speak to the Samaritan woman, and that she go preach him to the city Sychar in Samaria.

³⁵ do not say that it is yet four months, and the harvest cometh; lo, I say to you, Lift up your eyes, and see the fields, that they are white unto harvest already.

³⁶ `And he who is reaping doth receive a reward, and doth gather fruit to life age-during, that both he who is sowing and he who is reaping may rejoice together;

³⁷ for in this the saying is the true one, that one is the sower and another the reaper.

³⁸ I sent you to reap that on which ye have not laboured; others laboured, and ye into their labour have entered.

And here we see that the Samaritan woman was sent to be a part of sowing and reaping.  She preached the Messiah to the men in Sychar, and look what happened next:

³⁹ And from that city many believed in him, of the Samaritans, because of the word of the woman testifying, -- `He told me all things -- as many as I did.'

Many people from Sychar in Samaria believe in Jesus (reaping) because of the word (sowing) of the Samaritan woman.  She literally lead them to the Christ.

⁴⁰ When, then, the Samaritans came unto him, they were asking him to remain with them, and he remained there two days;

Jesus, a Jew, stayed with the Samaritans, even though that was politically incorrect.  Jewish men were not supposed to have any dealings with Samaritans.  Further, Jesus sent a woman to lead many in a city to Him.  This was also not politically correct (and still isn't today in many circles) yet God seeks His worshippers to worship Him in spirit and truth, and there is not male or female in Christ.

⁴¹ and many more did believe because of his word,

⁴² and said to the woman -- `No more because of thy speaking do we believe; for we ourselves have heard and known that this is truly the Saviour of the world -- the Christ.'