I found this information on an auction listing and 1000 appears to be accurate. This listing was for 921/1000.
First Edition; 1989. One of 1000 numbered copies signed by Bob Kane with an original ink drawing of Batman by Kane. The autobiography of the artist who created the immortal comic book character Batman in 1939Limited first edition copy of ''Batman & Me'' signed by Batman creator Bob Kane. Published by Eclipse Books: Forestville, California: 1989. Copy number 921 of 1000 of Kane's autobiography is signed on a special limitation bookplate, ''Bob Kane''. An original Batman sketch, also signed by Kane, is affixed along its top edge to the flyleaf. The 155pp. book, with a preface by fellow comic artist Milton Caniff, tells the whole Batman story, from the beginnings of the first cartoon in 1939 to Batmania and Batman the movie. Almost every page is illustrated; complete full color Batman comic strips fill the center pages. 8.75'' x 11.25'' book with blue cloth boards is housed in matching slipcase featuring a gilt Bob Kane autograph and Bat-Signal. mint conditionBob Kane Batman Sketch Original Art in Batman and Me Signed, Limited Edition Hardcover: Book 921/1000 (Eclipse Books, 1989). Bob Kane's beautifully rendered 7.5" x 10" black marker sketch of the Caped Crusader has been drawn and tipped into the frontispiece page of this handsome book. This piece is the perfect drawing for Kane's 1989, slipcased autobiography, Batman and Me, which was autographed and numbered, #393/1000 on a tipped-in flyleaf color plate. The book, sketch, and numbered plate are all in Excellent condition.