Luke 10:39 depicts Mary the sister of Martha "sitting at the Lord's feet" which is a Jewish phrase expressing discipleship. One who "sat at the feet of another" was that other's disciple (compare Acts 22:3, KJV or NRS). Luke 8:1-3 depicts women as part of His entourage along with the twelve. The evidence isn't terribly overwhelming, but Jesus was known to converse with women in a way that was culturally inappropriate (John 4).
My understanding has always been that Jesus was bucking the times; His teachings on divorce were apparently a correction of liberal Pharisaic practice of divorcing women for little or no cause (the issue was what was considered "indecent" (NIV) as per Deut 24:1), which would socially ruin them; they would have the shame of being unwanted, + having to go home to daddy, + being not-a-virgin for any subsequent suitors. In other words He was sticking up for their rights, which had the potential to be trampled on despite the protections in the Torah.
Paul lists other social barriers that were broken down at the end of Galatians 3. Jew, Greek, slave, free, male, female are all "one in Christ." Why would he bother to mention the male/female equality if it were not a new thing?
The Bible does have those lines about a woman not teaching a man, but then Priscilla is depicted as having ability/authority to teach (Acts 18:26 and, arguably, Romans 16:3). We have a woman in our own church history who has a lot of authority to teach.