Being an ally of Nazi Germany, Bulgaria wasn't occupied by it. That doesn't mean Bulgaria was completely independent of Germany, but Bulgarians had they say in their own policies, unlike puppet governments in Europe of the time. Roma story is kind of connected with that of Bulgarian Jews. The racial laws of the kind were introduced even before Bulgaria became German ally: Jews were declared second class citizens and were subjected to rather harsh treatment, many of them being deported to forced labour camps inside Bulgaria. However, they were never deported to the Nazi extermination camps: even after the government gave in to German demands, there was enough public pressure to reverse policy of deportation. That goes just for Jews of Bulgaria proper: Jews from the lands that Bulgaria annexed in 1941 (most of the modern Republic of Macedonia, parts of Greece) were deported in 1943 mostly to Treblinka. It's kind of similar story to that of the Hungarian and Italian Jews, with that difference that Bulgaria stayed out of the German reach in later part of the war (unlike northern parts of Italy or Hungary), so Bulgarian Jews were mostly spared extermination. Now, I'm not very informed about any English language sources on this, but you can start here.

Now, as Roma are concerned, they weren't targeted by initial racial laws, but after German pressure mounted they were also subjected to forced labour, marriages of between the Roma and Bulgarians were forbidden, and so on. But, they weren't deported to extermination camps, so they mostly survived the war. (You can check F. C. DeCoste, Bernard Schwartz. The Holocaust's Ghost: Writings on Art, Politics, Law, and Education, Edmonton: University of Alberta press, 2000, p. p. 191–192.

After the war Roma families kind of continued with high number of children, so their percentage in overall population became higher over the time.