First off, the Greek-Bulgarian border is not small, not by a longshot.
(Map as of the Doge War)
No idea what the state of the Greek army was back then, but we weren't in a good economic position after multiple national catastrophes and the odd bit of terrorism and economic collapse.
On the other hand, there were also lots of Bulgarians yeeted out from Thrace and Macedonia that will probably be happy to join in on smashing some Greeks.
Lots of veterans from the Balkan wars and WWI, too.
I think the main thrust will be towards Thessaloniki and the other north-eastern parts of Greece, thus giving us an useful bypass of the Bosporus, also, letting the Italians move through our territory will help their war effort and we can be used as garrison troops.
Considering the, oh 1500 years of bad blood between us and them and the stab in the back after the first Balkan war, well, they just might prefer to be occupied by Italians.