The Bulgarians were useful in the various Balkan campaigns, including Romania. This allowed Germany and Austria-Hungary to commit limited forces to the region and focus elsewhere, which since both were overstretched was useful. After 1915 Bulgaria as astride the line of communications between Germany and Turkey, which was really important, though conceivably a neutral Bulgaria could have let the Central Powers use their rail network.
Bulgaria actually joining the Entente side would be bad for the Central Powers and good for the Entente because they cut off Turkey. However, this would really only happen with a much more successful Dardenelles campaign, and that would probably knock Turkey out of the war anyway.
The Central Powers could promise Bulgaria pretty much any piece of territory they wanted -they even got some border concessions from Turkey- so while a Bulgarian government could have decided to sit out the war, it would have to be pretty determined on neutrality. For example, once Rumania joins in after the Brusilov offensive, it would have taken heroic restraint from a still neutral Bulgaria to not repay Rumania for what the Rumanians did in 1913.
But if Bulgaria is determinedly neutral, while not blocking German communication with Turkey, the effect would be that the Serbian Army could retreat south through Macedonia to Salonika instead of over the mountains, and what IOTL was the Salonika front would exist further north. Belgrade will still fall once either Austria-Hungary got its act together or Germany sent the 11th Army. But the Central Powers could not turn that front over to Bulgaria and that would have small butterflies elsewhere since the two or three corps would have to be taken from other fronts.
Bulgaria was punished for joining the Central Powers by losing their Aegean coastline. I have the impression that it was never really missed. If they stay out of World War II, that has even smaller effects on the conflict but a slightly greater postwar effect as Stalin has no excuse at all to force them into the Warsaw Pact.