During the final stages of the First Balkan War the only two European Ottoman territories left unoccupied by the Balkan League were the Gelibolu peninsula and easternmost Thrace (east of Catalca). When the Catlalca defence was formed, the Russians actually threatened the Balkan League (Bulgaria in particular) with war if the straits were to be threatened. Any (semi -ASB) breakthrough of Constantinople's last defence would lead to an intervention by the Great Powers.
Bulgarian interest were mostly focused on Macedonia (where most ethnic Bulgarians in the Ottoman empire lived, but were unable to become part of Bulgaria after the Berlin Congress) but the Balkan League logistics required their army (as the strongest of the Balkan nations) to engage the bulk of the Ottoman defence south of former East Rumelia in Eastern Thrace. Hence the reason almost no Bulgarian forces were sent into Macedonia and these regions were left in Serbian and Greek hands.
Cooperation beteween the Balkan allies was low and despite the victory, the Bulgarians were left with only a small chunk of their desired Macedonia, (Pirin and Strumica) the rest going to Serbia and Greece. One of the few pre-war agreements was the division of Vardar Macedonia between Serbia and Bulgaria along the Ohrid - Kratovo line. As we all, know the Serbs recieved an ultimatum from Austria and Italy (both feeling threatened by a potential Adriatic coast of the Russian backed Serbians) to pull out of Albania. And thus Serbia, left only with Kosovo and half of Novi Pazar refused to honour this agreement and annexed lands further south-east of the proposed line.
Even though Bulgaria gained all of Thrace, a large chunk these lands (even to this day) are populated mainly by Turks. An enlarged, exhausted, post-war Bulgaria with a significant Turk minority is bound to cause ethhnic tension.
If OP is trying to avoid the Second Balkan War for the sake of Bulgaria's prosperity post-war, then this could be achieved more plausibly another way. Maybe have Serbia or Greece being left unsatisfied by their spoils. Maybe with promises of war indemnities and maybe even South Dobrudja we can have Romania join the Balkan League (even though this would definetly attract the Great Powers' attention as this alliance would be getting too influential). This way Bulgaria would be able to spare more forces for Macedonia and gain Salonika and Ohrid. Then have Serbia or Greece feeling betrayed and thus attacking their allies, then getting ganged up on ... . On the other hand if OP wants to avoid the Second Balkan War as a whole, maybe the most plausible scenario would be to improve cooperation between the Balkan Alliance participants pre-war, but even if war is avoided it is (nearly) impossible to satisfy everybody.
