Probably from Old English. Compare Old English berwinde for the first element (which might be related to Old English bere (“barley”) or bearo (“grove”)) . For the second part, compare other names for the same plant such as English cornbind and withwind, which seem to show free variation between wind and bind in compounds.
bearbind (uncountable)
Part or all of this entry has been imported from the 1913 edition of Webster’s Dictionary, which is now free of copyright and hence in the public domain. The imported definitions may be significantly out of date, and any more recent senses may be completely missing.
(See the entry for “bearbind”, in Webster’s Revised Unabridged Dictionary, Springfield, Mass.: G. & C. Merriam, 1913, →OCLC.)