Blacklip oyster is an item miners find in grade 3 and grade 4 nodes. (I have personally found them on grade 4 nodes but was unable to extract them, but did manage to dig up some wyvern obsidian and damage 2 chunks of darksteel ore).
So 25+ miner may be able to get some for you down the road.
The spiders do drop them as well, but there seem to be about about 4 spiders per continent.
Central Thanalan near the mine has 4 spiders (2 on each side of the upper area overlooking the mine entrance). These share placeholders with marmots and can go for 20-30 min before they repop (other times they can repop back to back in only 3 minutes). I went 2 for 10 on the oysters from these spiders and made some weapons for my LS.
The second place to find killable spiders is north of the level 10 forest camp (I forget the name). Agan there seem to be two spots where a pair of spiders pop, but I didn't explore this area much. The spiders are heavily camped in both areas, usually 2-3 people at any given time waiting for them to repop.
Best advice? Forget about the bone weapon. They are the weakest crafted weapon in the entire game and they are not worth the trouble. Save you money for leather or bronze, which should be getting more common as more leather workers hit the 20-25 level range. Don't feel bad about using your starter weapon until then... SE simply **** the bed on low level crafting recipes.
PS. If you are really impatient an NPC vendor sells the leather PUG weapon for 80k. Many PUGs bought their weapons like this due to the flawed crafting system and it's inability to meet the demand for low level weapons.