I don't think Churchill had much directly to do with the decision to bomb. Once the idea of a Baltic front was dropped by the allies, Bulgaria became a very low priority for Britain and was accordingly managed at a lower level of government that didn't involve Churchill.

Marietta Stakova, in her book 'Bulgaria in British Foreign Policy, 1943–1949', notes that the UK War Cabinet rarely needed to make specific decisions about Bulgaria with the few references to the country being routine information-only reports given by theatre commanders.

Essentially Bulgaria fell into Britain's general strategic aim to split the satellite countries away from the axis. The problem for Bulgaria was that it didn't want to give up the territory it had gained when it joined the Axis, and it was betting that the axis would win the war. That meant that Britain's Foreign Office didn't have much diplomatic leverage. That left force, so Sophia gets bomber raids.

In terms of post-war positioning, Churchill and Stalin reached agreement that Bulgaria would be 80% Soviet sphere of influence. This is another reason why Bulgaria didn't rate too much British interest.