I've done some looking into this in the past. By far the best-documented discovery of a dinosaur bone from before the 19th century is in a book from 17th century England. I'm going to copy/paste the relevant part from a previous comment of mine because you'll be really interested in it. The view of the scientist/naturalist at the time? It belonged to a giant!

"The first scientific illustration of a dinosaur fossil was published in 1676— just the fossilized end of an enormous femur— by a man named Robert Plot, in his book, Natural History of Oxfordshire. Darwin's Origin of Species was of course very far away, but the idea of extinction at all, much less evolution, had not yet been recognized. Most people were creationists who believed that all the animals currently on Earth were the same set of animals that had existed in the very first days of Earth's history.

So, Plot knew that the fossil had once belonged to a real animal, but his only options to choose from were all the animals that he knew existed in the world and had been to England. At first he thought it must have been a bone from an elephant brought over by the Romans, but when the size didn't match a live elephant he saw in captivity, he concluded it must have belonged to a giant human, like the biblical Goliath and other classical very large people.

It sounds a little silly, but all of his reasoning is very scientific and thought-out. His book is online here, and the dinosaur stuff starts on page 132. Here are some relevant quotations:

And that indeed there are stones thus naturally fashioned, must by no means be doubted... [but] none of them, as the judicious Charles Marquess of Ventimiglia well observed, [have] any signs of hollowness for the place of the marrow, much less of the marrow itself. Which has fully convinced me that this stone of ours was not so produced, it having those signs exquisitly expressed; but must have been a real bone, now petrified...

But against this opinion of its having been once a real bone, there lies a considerable objection, viz. that it will be hard to find an Animal proportionable to it, both horses and oxen falling much short of it... If so in probability it must have been the bone of some Elephant brought hither during the Government of the Romans in Britain.

But... there happily came to Oxford while I was writing of this, a living Elephant to be shewn publickly... with whose bones and teeth I compared ours; and found those of the Elephant not only of a different shape, but also incomparably bigger than ours, though the Beast were very young and not half grown. If then they are neither the bones of Horses, Oxen, nor Elephants, as I am strongly perswaded they are not, upon comparison, and from their like found it Churches: it remains, that (notwithstanding their extravagant magnitude) they must have been the bones of Men or Women. (pg 136)"

This does fulfill the 'pre-1800s' part of your question, but probably doesn't quite qualify for the 'less scientifically advanced' part, since Plot was making every effort to be scientific. Now, there are a large number of pop-science dinosaur books that regularly make the claim that dinosaur fossils have been discovered in China going back to antiquity and been assumed to be dragon bones, and used in traditional medicine. But, I've never actually seen any reputable citations of sources saying this. Someday I really hope to make the acquaintance someone who can actually look at Chinese archives for any descriptions of dragon bones like this, but I haven't actually seen any in English at all.

I also think the connection people often make between dinosaurs and european dragons is overblown, and that instead depictions of dragons shifted in the 20th century to resemble dinosaurs as dinosaurs became famous and well known. Pre-modern depictions of legendary creatures like dragons usually seem to be way smaller than the famous dinosaurs, and usually don't have too many dinosaur like features, often having mammal-like ears, snouts, batlike wings, etc. Though it's possible they used mammallike traits in art because the fearsome creatures they were familiar with like wolves and lions were mammals.

Then there are also some books or websites alleging that there are Classical depictions of dinosaur fossils (this pot, for example). This is probably the most reputable-looking one: The First Fossil Hunters: Dinosaurs, Mammoths, and Myth in Greek and Roman Times. I have not read it, so while I'm skeptical I shouldn't comment on it. Both of us should look into it!