The first Sino-Japanese war was basically a war over influence in Korea, and "bad blood" had little to do with it.

Contextually, it was the age of imperialism, and the Japanese leadership had decided that becoming an imperialist power was pretty much the only way to avoid falling victim to Western imperialist nations (indeed this proved true, as victory in the Sino-Japanese war helped Japan renegotiate its unequal treaties). Japanese expansion began almost immediately after the Meiji restoration, with expansions into Ezo, now known as Hokkaido, and the Ryūkyū kingdom, now known largely as Okinawa. In 1876, after an episode of Gunboat diplomacy called the Un'yo Incident, the Japanese imposed on Korea the Treaty of Kanghwa, an unequal treaty largely modeled on the one that the US had imposed on Japan 18 years earlier.

As Kirk Larsen has recently argued, China had also been trying its hand at western-style imperialism, expanding its traditional tribute relations with Korea into a kind of informal imperialism by directly intervening to protect its influence and trading rights there.

Korea at the time was exploring ways to respond to the sudden presence of militarily powerful actors with exploitive economic aims in the region, but was largely divided about how to go about it. Some Korean leaders wanted to maintain their long standing ties to China, while others wanted to model their developmental course on Japan, seeing its relative success in dealing with the West and industrializing. There were also pro-Russia groups, but these came to the fore later. These positions were also associated with the factional infighting in the Korean court, and tensions gradually increased through a long and confusing series of struggles, each involving different factions with backing by Japanese and Chinese actors hoping to increase their influence and economic rights in the region.

One such struggle, the pro-Japanese Kapsin Coup of 1884, which attempted to liberalize Korean society and do away with the traditional class distinctions, managed to take the royal palace, at which point the conservative elites called in Chinese (Under general Yuan Shikai) help to put down the coup. The two main outcomes of this were an extended period of Chinese influence in the Korean court and the Convention of Tientsin (Tianjin), in which both China and Japan agreed to withdraw their troops from Korea and to notify the other before sending troops in again.

Along came 1894, and there was another uprising, this time led by the syncretic Tonghak religion, with anti-foreign, and generally populist goals (down with the exploitive traditional hierarchy, all men are equal under heaven, etc.). Once more, the Korean elite called for Chinese aid in putting down the rebellion (later turned out they didn't need it), so China sent troops. Japan claimed that violated the earlier convention, and sent troops of their own. China claimed Japan baited them into sending troops. Either way, there were now quite a lot of troops in Korea, leading the whole thing to spin out into the war itself.

Edit: Now, tied in with Japanese imperial expansion was a growing discourse of Japanese superiority among Japanese leaders and intellectuals. Certainly, elements of that discourse that helped justify influence in Korea (they're "backwards," Japan is "modern" - kind of a "yellow man's burden" argument) and a general poor opinion of Japan's Asian neighbors. Japan was adopting the Western vision of a racialized hierarchy of civilizations and self consciously using a discourse of "modernization" to place themselves higher on the ladder than other Asians, equal or almost equal to Europeans. The attempt to portray the Japanese as more "civilized" than their Chinese opponents can be readily seen in the images in John Dower's piece on Sino-Japanese War prints and propaganda (ctrl+F "routing the foe"). The arrogance of that ideology (not to mention the violent territorial expansion that went with it) definitely went a long way in creating bad blood in the region.