In fact, I do not see Bulgaria joining the Entente, but will continue to join the Central Powers (their unitary lands such as Vardar, Macedonia are with the Serbs)
But the Ottomans saw them as much more likely to join the Entente if Italy joined the Germans (they hated the Russians for a long time and this is true, but the memory of taking Libya is still very close)
And the Ottomans will say to Wilhelm II, "Nothing personal, but we hate the Austrians, the Italians, and the Greeks more."
In order to make Italy join the Germans, the Turkish-Italian war must end with an Ottoman victory, and therefore not the First Balkan War. This means that the Greeks and Bulgarians join the Germans if the Ottomans join the Entente
Without the blockade of the straits, the Russian situation would be greatly improved (unless you replace it with a Swedish blockade of St. Petersburg)