The complete title of "Ancient Music" is this:

Full descriptive title: A General Collection of the Ancient Irish Music, Containing a Variety of Admired Airs never before Published and also the Compositions of Conolan and Carolan, Collected from the Harpers &c. in the different Provinces of Ireland, and adapted for the Piano-Forte
        

Notice that 'adapted for the piano-forte'. I don't know what Bunting did to adapt the melodies, but he makes it clear that his MS is not a collection for the harper.

I scanned the 66 tunes in Vol 1, and there was only one tune in E. There were 6-10, I'd say, in A and the same number in Eb. Most are in simple keys.

With respect to the gathering of harpers in Belfast in 1792, he says he was cautioned not to change a single note. (This is in the Preface.)