I plan on building a large base in Minecraft that will involve some white and gold in some parts, and while a gold farm in the nether will do for the gold blocks, I still want to have some bone blocks in place of white concrete for some texture. I know that I can make automated villager carrot or potato farms, then have the food go into an autocomposter which would make bone meal that I could craft into bone blocks, or have a mob farm to produce bones to craft into bone blocks. I need to know which one would be more efficient, but I would like it to be fairly cheap and I am still early in the game, without many resources. Does anyone have any suggestions or designs for a bone/bone meal farm that would work best for this?
An efficient general mob farm. Something like Gnembon's.
Finding fossils in the overworld is simply ludicrous as an advice. The are very rare, you may spend months playing and never find a sinfle one - and once you find it, you get what - half a stack of bone blocks?
Soulsand valley is a more reasonable advice - once you find it, you'll be able to obtain a couple stacks, although being harassed by ghasts and skeletons will make it rather unpleasant (and once they are gone, you'll need another Soulsand Valley).
A skeleton spawner based grinder - providing you find such a spawner - will produce about 12 bones - or 4 bone blocks per minute, that's about 240 blocks per hour. Acceptable, but still very far from "best".
The mob farm produces 1800 bones per hour (besides all kinds of other goods) - that converts to 600 bone blocks per hour. And you can build better, faster farms and get bones even faster.
There are several ways you can get your hands on bone blocks:
Find a Soul Sand Valley. This is a biome located in the Nether, and has a very large amount of bone blocks coming out of the ground. This is arguably the best way, but it has plenty of skeletons, so be careful!
Find fossil remains. Fossil remains are structures made of bone blocks, similar to the structures in the Nether. They typically generate in dry areas such as the desert and are generated from Y 40-49.
Craft bone blocks. This is very inefficient and will take a lot of time, unless you have a skeleton grinder set up. You simply craft them by placing 9 bonemeal in the crafting slots, like so:
Those are the only methods I am aware of to get this block.
The best way is to make a zero tick kelp farm (Google/YouTube search for a tutorial that works with your version) and put composters in place of the smokers. Using this method you can make a stack in a minute or two it also is essentially endless as you just flip the switch and it makes bone meal until your chests are full.
You will have to replace broken kelp from time to time in most of these setups.