The major benefit to a "Greater Bulgaria" emerging from the Second Balkans War is that it will likely sit out of both World War I and World War II since it has no revanchist claims.
Instead, it might even opportunistically join the Allies in the late war (say September 1918) and seize Thrace and even perhaps Constantinople.
Avoiding WWII is harder because of German pressure to align with the Axis, but it won't be stained with having attacked Yugoslavia. It likely though has to agree to German transit through Bulgarian Macedonia so the Nazis can attack Greece to help out Mussolini. However, internal Bulgarian politics might be more moderate since you won't have ultra-nationalists being attracted to fascism to recover Bulgarian lands. With a better balance in the government, it is at least plausible Bulgaria declares war on Germany and gets Western Allied support (and perhaps a parachute detachment into Sofia) before the Red Army reaches its border. It's likely the monarchy will survive.
That would leave a non-Communist Bulgaria open to Marshall Plan investment, NATO and earlier EU (in whatever its earlier forms were called at the time) membership, and Western reforms. Worst case scenario would be an economy equivalent to Greece. Best case is probably around Spain.
It would not even be considered a regional power, but it'd be the most important country in the Balkans and a leader in the Black Sea. It would likely be the most important country between Germany and Russia with Poland a close second (assuming the collapse of Communism and Soviet Union as IOTL).