How long did it take to copy a Bible during the early propagation of the Christian faith?

In the earliest years of the newborn Christianity, scribes wrote on single sheets of papyrus, formed into scrolls, or birch bark sheets. Towards the end of the 1st century a.d., parchment, made of animal hides (the best type known as vellum, whose root is shared with veal, or calf). While papyrus did continue to be used perhaps as late as the 9th century, by the 4th century a.d., parchment had taken over as the writing sheet of choice. While the scrolls had sufficed in the beginning, as the tomes grew in size, it was discovered that many sheets of vellum could be bound into a codex, or book. As Europe descended into what is called the Dark Ages, illiteracy took hold throughout Europe. Even the leaders were mostly unlettered. Only the monastery remained truly literate, with monks acting as the scribes. Parchment, or vellum, was chosen for the books due to its durability, as compared to the much more brittle papyrus.

• Vellum
  To make one sheet of vellum, a parchmenter would start with the skin of a calf and soak it in running water overnight. It would then be put in lime water for about a week, then brought out and scraped for a day or two. Soaked in lime water a second time and scraped again. Finally, it would be put back in the clean running water for 2 days and then mounted on a frame a scraped again for days. As it dried while being scraped clean, the parchmenter would sand it and pumice it. This whole effort might take two to three weeks. For one single sheet of vellum.

• Writing Utensil
  Quills were usually made from the outer feathers of a large bird, a goose or swan. The chosen feathers (only a few, 5 to 10, per bird, were usable) would be plucked. The barbs then scraped clean. The remaining shaft would be hardened by heating and cooling in a sand pit.The remaining hide would be scraped off, the tip would be cut at an angle and then carefully split. This whole process would take maybe a day for 10 or 20 quills. A scribe would continuously sharpen the quills end throughout the days writing and one might last a single day.

• Medium
  Ink by itself on a sheet of vellum simply would not work. It would not adhere to the material. So a medium would be needed. Two commonly used mediums were Gum Arabic, which you may have heard of, and something called Egg Glair. Gums were made from the gum, or sap, of several kinds of trees. Egg Glair from egg whites. These were used to help fix the inks and pigments to the parchment.

• Pigments
  For illuminated texts, gold leaf and pigments were needed. The colored pigments were made from things like shellfish and precious stones ground into powder. There were also (poisonous) chemicals used in the creation of other colors, such as mercury and sulfur.

Creation of the codex
In the 9th century, Benedict began encouraging his monks to read and write and collect the religious knowledge so that it would not be otherwise lost. Through the 11th century, monks, sitting in the cloisters, studied the scriptures and copied them for other libraries. Scribing was not all a monk had to do all day. There were several prayer sessions, gardens had to be tended, food prepared, and the vellum and quills made. A single scribe, it is estimated, could write as two or three books a year.
As time went on, the scribes improved their processes, until by the end of the manuscript era in the 15th century, a book could be written and illuminated in as little as a few days. One of the fastest known writers in the 15th century boasted he could produce the old testament in three days.

Most books written during these years (the 9th to the 15th cent.) were at the very least decorated, with the more important ones being illuminated with gold leaf and pigments. Gospel books (new testament), the tanukah (old testament) and psalms were almost always illuminated.

From the 9th through the 15th centuries, or the manuscript era, the materials remained basically the same as listed above. If a single scribe were to make his own vellum and quills, many months would be required just for those tasks. Of course, in practice, the parchmenter made the sheets, another would make writing utensils, another the inks, etc.

In the earlier years, of the era, where monks alone were the scribes, as I said, it would take the better part of a year to make one or two copies of one book, since a monks day was never just writing. As the years passed, and secular persons were used, who could concentrate on only writing, the time required was shortened.

As Mr. Durden pointed out, there was no such thing as the Bible as we know it, not even through to the end of the manuscript era. The testaments were (usually) separate, as was the apocalypse, the psalms, etc. It wasn't until the print era (typesetting) that everything was combined into one work. If you were a landed noble (i.e. wealthy) you might contract a codex of the gospels and get it in a year's time. (but probably not, as you most likely couldn't read anyway.)

• Sources

Medieval Manuscript Production: Scribes, Illuminators and Their Methods of Work by Duchess Althea Charle, O.L.

The History of Visual Communication, Sabanci University, Istanbul, Turkey

From my local university library,
Medieval Craftsmen-Scribes and Illuminators, by Christopher de Hamel, 1993

and finally Wikipedia