Bulgaria is really easy, historically it came down to the wire on which rite they'd follow and to whose authority they'd submit. In the end they got an autocephalous patriachy and followed the Eastern Rite, but if the Pope had been less obfuscating towards (and I can't remember his name here, can someone help me out? He was a chronicler of the Ottonians and hated the Eastern Emperor, and I think he was from Pavia) a certain priest, the Bulgarians could've become Roman Catholics. I believe the King of the Bulgarians was interested in it at the time, but the Eastern Emperor was able to act in the absence of action from the Pope.
This is very interesting. I would suspect that a Roman Catholic Bulgaria would almost inevitably lead to Roman Catholic Vlach, Serb and Slavic Macedonian peoples and use of latin script for all their languages.
Now the straits and Constantinople itself would have remained under ERE and Orthodoxy. So this leaves conversion of Kievan Rus to Orthodoxy likely. However, if we go by the thinking in Harry Turtledove's "islands in the sea", Bulgaria's adoption of Latin Christianity could have knock-on effects extending to a Latin Christianity Russia as well.
I suppose the Bulgarians might have been receptive toward the western version of Christianity at the time because the Frankish Empire was fairly large and powerful at the time, but not so close they were fighting, whereas the Bulgarians had fought and beaten the ERE several times.
Of course, when the ERE under Basil comes back to crush the Bulgarians in th 10th century, it's going to be even nastier for the latter. And, there may be a lot of outrage against the the ERE for the act, perhaps leading to some Serbian and Magyar "crusades" against the ERE.
I don't see a reason why there would not be an ERE resurgence defeating the Bulgarians (and tag-teaming them with Sviatoslav's pagan Russia), so that will be a poor advertisement for Latin Christianity in Russia.
It's interesting to me that that the formal schism is not dated until 1054, because there were clearly differences in terms liturgy and sense of identity going back to the the 8th century, as stories about competition for Moravian and Bulgarian adherence to western or eastern churches attest.
Indeed, while one version of the Russian adoption of eastern Orthodoxy story shows Islam and Judaism as the main competitors the Rus rulers investigated, another account names the competitors as Roman Catholicism, Greek Orthodoxy and Islam. And the splendor of Constantinople's cathedrals to Germany's more austere Catholic churches accounts for the eastern version's greater appeal in Russia.
--So, Bulgaria joins Latin Christendom- that is going to change a lot of European history rather quickly, but even if many, many convergent outcomes occur (Bulgarians crushed by Byzantines and later recovering, Kievan Rus adopting Orthodoxy, western Crusades, Turkish Islamic conquest into the Balkans, emergence of Russia as a major power), the modern relationship of Russia and the Balkans will certainly be very different, and sentimental ties will not emerge between Russia and the Balkans slavs will not emerge over shared religion, but only over ethnolinguistic affinities, if that ever even becomes a thing in the 18th, 19th, 20th or 21st centuries. So, any Russian slavic brotherhood with Bulgarians or Serbs only runs as deep as Czech-Russian brotherhood.