If Bosnia isn't occupied by AH in 1878, then it probably becomes an autonomous principality under hybrid Christian-Muslim administration, while some small parts are ceded to Montenegro and maybe Serbia. From there on it's hard to guess at how things might develop in Bosnia. The native regime would probably do better at addressing social problems when compared to Austria-Hungary's administration in OTL, but it might also be more corrupt and less stable.
This also removes OTL's major bone of contention between Austria and Serbia. As a result the pro-Austrian Obrenovic regime stays in power in Serbia. (King Milan and his son were capricious rulers with questionable ideas on democracy and foreign policy, but without this part of the backlash their worst qualities wouldn't really come into play and they'd be only mildly unpopular. Thus the rival Karadjordjevic is never called to take the throne of Serbia, although they might still have a profitable career in Montenegro or Bosnia.)
The Ottoman Empire doesn't gain much by this change. There will probably still be a Balkan War to drive it out, but at a different time, due to Austria's greater influence in the Balkan states - it'll happen if and when Austria gives the green light and will likely involve Austria itself, slightly expanding its territory and greatly expanding its zone of influence (up to Thessaloniki?). If the autonomous principality in Bosnia isn't annexed by someone or broken apart by internal conflicts, it will likely be partitioned between Austria and Serbia at that point.
Not sure how this influences the relationship between Russia and Austria. Both will be in favor of the status quo for some time, but that doesn't prevent jockeying for influence and tripping up each other in the Balkans. In theory, Russia's desire for control over the straits and Austria's likely desire for a zone of political and economic influence stretching to Thessaloniki aren't incompatible, but in practice they could still turn out hostile.