Technically speaking, the Glagolitic was created a few years (just a couple years, actually) before the conversion of Bulgaria to Christianity, due to the request of the Velikomoravian knyaz Rostislav for the Byzantines to send a mission of their own to Great Moravia. This was in 863, a rather complicated time, during which the Germans and their ally knyaz Boris I of Bulgaria were (again) fighting Velikomoravia (modern Slovakia), which itself saw Byzantium as a potential ally.
Hence, the two Byzantine brothers from Thessaloniki (whether their mother was Bulgarian, as their Life claims, or not, is irrelevant – they were more than clearly in Byzantine service) created the Glagolitic with Great Moravia in mind. Only after Methodius’ death and the following German persecution did his Bulgarian disciples (and probably most of his other Slavic disciples, including his Moravian successor Gorazd) return to Bulgaria and bring the Slavic writings here, where they eventually found a most fertile soil.
And while St. Kliment of Ohrid is indeed often accredited with devising the Cyrillic alphabet, it seems more likely that he actually created an easier to write form of the Glagolitic script, the so-called Rounded Glagolitic (I think that’s the same kind which the Croats used until the 18th century or so), which is exactly what his Life says. As for the Cyrillic – considering its oldest finds are from the area of the Preslav Literary School, which itself was traditionally more inclined towards it (while the Ohrid Literary School kept using Glagolitic for a few centuries longer, until the early 13th century or so) and considering the Cyrillic script is obviously based on the Greek one, I think it’s more likely that the Cyrillic script was devised either by St. Naum or, more likely, by some of the disciples or clerics who had spent time or received their education in Constantinople. Besides Tsar Simeon the Great, it also seems likely that f.e. Yoan Exarch had also studied in Tsarigrad (and potentially a few other notable figures as well), and there’s also the report of those disciples of St. Methodius, who were originally sold to slavery in Venice, but were bought by a Byzantine noble there, sent to Constantinople and after awhile most of them were allowed to go to Bulgaria, where they surely would have taken part in the active cultural life of the country.
Anyway, the Glagolitic alphabet was created with Velikomoravia in mind (though it’s not the script itself that’s most important in all of this – the deeply Christian symbolic meaning of the Glagolitic script itself hints at the motives and purpose of it, whereas the Cyrillic is much less religious in character; hence the irony in modern retrospect of Chernorizets Hrabar’s claim that the Slavic letters are holier than the Greek), though its seed managed to find good ground only in Bulgaria (and from there – to other places as well, like the aforementioned Croatia), it was eventually simplified with a new, easier to write form in the Ohrid School, while the Preslav School “simplified” it by largely replacing it with derivatives of the Greek alphabet, which had its own century-old tradition in Bulgaria. Eventually, this Cyrillic script became much more popular than the Glagolitic script, which it replaced in a couple of centuries, and we’re still writing on it to this day (though with several further waves of redactions, of course, the most influential of which is probably Peter the Great’s “civil script” and, respectively, its cursive form). While it’s interesting to note that Moravia (Slovakia) nowadays uses the Latin alphabet instead, which I find somewhat ironic, considering they could’ve become the cultural and spiritual centre of the Slavic world.