Unless there are people in the church that were there at it's founding, then yes today the churches beliefs come from the bible. It's not a book that a bunch of early catholics decided to write random junk in. They were very specific about what went into the bible to ensure that the lay person and the future clerics of the catholic church knew where to find what it is the church believes. And at this point, there is some questions as to what was intended by choosing certain verses because, of course, there is no one alive today who was alive when the bible was put together. Which means that anything that is not inarguably clear has the potential of at some point being interpreted in another way.
I don't know where I said the church comes from the bible, I did say the beliefs come from the bible though. Maybe I should have said that today the beliefs come from the bible.
With regards to women as priests until the 4th century, there is some indication that the catholic church may have had female priests prior to the 4th century. Women were not officially banned from Priesthood until the Council of Laodicea in the 4th century, something I posted above.
One does tend to see, at least in North America, a tendency for Catholics to argue from Scripture alone. I think this is probably because in many cases they are apologizing to fundamentalists, or have been influenced by them. But it is not really a Catholic way of thinking.
Re banning of women as priests - it is important to remember how the Church typically defines doctrine - at least historically. Historically doctrine is only formally defined in response to a heresy or misunderstanding. A 4th century ban against female priests would suggest a local heresy or schism involving ordaining women - not necessarily a change in policy. Laodicea was a regional council, which suggests a regional issue.