To find out how many allied aircraft were shot down by Doras, you'd really have to add together the indivdual scores of each pilot who flew them and work out how many he got in the Dora. Probably a difficult thing to do.
As a previous poster mentioned, other 190 models were adapted for dealing with bombers, as were entire groups and tactics. These "Stormgroups" used heavily armoured 190A8s (Sturmbock) with a lot of fire power. They had orders to approach the bomber formations from behind, line abreast and not to open fire until very close. These aircraft carried over two hundred pounds of extra armour, including extra bullet proofing on the canopy. They were supposed to ram the bombers once their ammunition was expended...
In this configuration, the 190 was no match for the escort fighters. The Luftwaffe used mainly 109Gs to try and tempt away the escorting fighters. If you were wondering why the 190 jumped from the Anton to the Dora, the reason was that the B and C versions, though made and flown, never reached the production stage. They were both inline versions, like the Dora, conceived for high altitude performance. The Radial engine used in the A series (BMW 801) wasn't so good at high altitudes and a solution was sought in inline engines. This resulted in the "B" variant which used the DB 603 as well as some experiments with nitrous boosted radials(!). The project was abandoned and supplanted by the "C" which was basically an improvement on the "B" with inline engine. Six were built in various configurations. Things finally came together with the Dora. Fitted with the Jumo 213 and based on the A7 airframe with a stretch, the 190D prototype went into pre-production, then production as the 190D9 with changes made in the fin design, canopy and the addition of 13mm guns in the cowling. This is the model we all know and love (well maybe not all of us).
I may well have got some of this slightly wrong, as it's mainly from memory of what I've read and studied but in general it should give an idea of the difference between the Anton and the Dora.
KD