It seems the 'me' designation is acceptable after all. I just did a fair bit of research and it seems either the 'bf' or 'me' designation is acceptable.

I think we can't tell for sure which plane was superior. Both side will say that our plane was better than the other. As the RAF evaluation of captured 109's , I truly can't believe the results they published cos surely it must be propagada at some point and you can't say to your pilots that their planes are inferior in any way not good for morale. Also they tested damaged planes and was the test pilot really pushing the aircraft to the limits ? Too much variables and the only way to know the truth is to view the BOB live but we can't go back in time so.....

Me is shorthand for Messerschmitt as Do is to Dornier, Ju to Junkers, FW to Focke-Wulf and BV to Blohm & Voss, etc. They were (and still are) valid shorthand for the German manufacturer's names.

The Bf in the Bf109 comes from the "Bayerische Flugzeugwerke" before the name was changed to Messerschmitt. In some cases the Bf was simply maintained as it was used in the early stages as far as I know. So both designations are correct.