All I can tell you about recordings is that almost all will be arrangements of the version A L Lloyd introduced to the Revival.

The tune widely known today isn't the only one to which forms of the song used to be sung, though. There is another version of the song in the DT:  BONNIE BLACK HARE.  It was noted by Dr George Gardiner from Thomas Jones of Portsmouth, Hampshire in 1907, though the DT file doesn't mention any source. Text (verse 1 is from Mr Jones, the rest is from a broadside edition) is copied from Frank Purslow, The Constant Lovers (London: EFDS, 1972) though with "bonny" altered to "bonnie" throughout; maybe that's why you didn't find it. The 3/4 tune is included in midi format, and is completely different from the one you know.

If the midi isn't working, you can get midi, staff notation etc at the Digital Tradition Mirror site:  Bonnie Black Hare.

There is some discussion of the two variants in thread  Tune Req: Bonny Black Hare.  It's a fairly rare song in folk song collections, for obvious reasons, but has turned up occasionally over the years. Cecil Sharp got a version in 1908, again with a regular tune in 6/8.