If 'bidi' means RTL, I can think of an African script. The Mende
Kikakui Syllabary (devised ca. 1917) of southern and eastern Sierra
Leone is written RTL. The direction of writing was influenced by the
Vai syllabary (devised 1832/33), which was at one time written RTL (but
today only LTR), and Arabic. One of the chief early uses of Kikakui was
for the transliteration of suras from the Koran, so RTL made sense.
While I called it a syllabary above, actually the first 42 characters
form an Abugida, the remaining 150+ form a syllabary.
For a somewhat recent publication on Kikakui, see:
Konrad Tuchscherer, "African Script and Scripture: The History of the
Kikakui (Mende) Writing System for Bible Translations", _African
Languages and Cultures_, 8, 2 (1995): 169-188. [deals with research with
over 100 Kikakui literates from 1990-94]