I think it's feasible for Bulgaria to gain Alaska, maybe bits of the Pacific Northwest, maybe a few Pacific Islands, although there's the long distance of Siberia to consider which will limit their effective control and potential settlement over the areas, and not to mention the threat of the Mongols. Oh wait, you mean European Bulgaria...
Bulgaria absolutely needs Greater Bulgaria to happen. This means the 1878 San Stefano borders from the start. Bulgaria then needs to beat the crap out of all other Balkan Powers (including the Turks) to gain most of Albania and Constantinople (perhaps more politically viable than letting Russia hold the place). Now you have a Bulgaria that might be able to project power, since they'd dominated the Balkans and the only goals left to achieve there is to keep their neighbours from overturning them. Unfortunately, I think that that will occupy the full attention of Bulgarian politicians and strategists, preventing them from joining the Scramble for Africa. If they did, I think Cyrenaica is the only part they might be able to get, since it's associated with Ancient (Christian) Mediterranean civilisation and is out of the way but relatively close to Bulgaria.