My usual first stop in trying to deal with such issues is the Conway's History of the Ship series. I just checked the relevant volume, Cogs, Caravels, and Galleons: The Sailing Ship, 1000-1650, and found no reference to bottom treatments. So far as I know there's scarcely any hard contemporary evidence on the subject. So I'll have to fall back on that most unreliable of sources, my senile memory.
I've read in several places (don't ask me where) that there were several common bottom treatments prior to the introduction of copper sheathing. I've never read that there was any clear chronological sequence to them; some or all of them probably were in use at the same time. One was a particularly repulsive-sounding concoction containing tar, sulfur, and horse hair (presumably in the hope that shipworms would find it disgusting and indigestible). Another was white lead paint; another was tallow - perhaps applied on top of the white lead. (I imagine tallow applied directly to wood would look like a semi-transparent grease; I figure slapping it on top of a coat of white paint would result in a slightly creamy off-white color.)
I don't know which of those treatments would be more expensive.
Some of the oldest surviving English ship models have white bottoms. Whether that was an accurate depiction of reality or a model builder's convention I don't know. (A modeler with any aesthetic sense would be turned off by the thought of reproducing that tar/sulfur/horse hair mix.)
There are four genuine surviving ships from the period covered by the Conway book: the Gokstad ship, the Oseberg ship, the Mary Rose, and the Wasa. The two Viking hulls clearly were unpainted except, perhaps, for some decorative carved work. Fred Hocker's book on the Wasa states quite emphatically that no waterline is marked on her, and the wood on her bottom looks just like that of the upper works I've read quite a bit about the Mary Rose, and I've never bumped into any reference to paint or other treatment on her hull.
The bottoms of hulls are rarely visible in old master marine paintings (e.g., those of the Van de Veldes), but I think I've seen some that appear to be white.
Brian Lavery's book, The Construction and Fitting of English Ships of War, says that by the early eighteenth century two coatings were in use: "black stuff" and "dark stuff." Apparently they were about the same as the two I mentioned earlier. Lavery says that "black stuff" rarely shows up in models, but he seems to think it was used more often than "white stuff" in reality. And he suggests that some ships may have had "black stuff" on their bottoms, with a band of white (for looks, I guess) just above and below the waterline.
I think this is one of those questions that don't have good answers. The good news is that you can paint the bottom of your model whatever color you like (though I'd discourage pink and purple), and it's highly unlikely that anybody can say definitively that it's wrong.
I'm afraid I haven't helped much.