Wiktionary
vb. (context usually with "to" English) To have a reasonable claim; to seem likely.
Usage examples of "bid fair".
In a week's time, Alcuin's wound had begun to knit and bid fair to heal cleanly, although it would leave a fierce scar.
Croaker skipped alongside, grinning and grunting, and bid fair to bounce my advisor from his shoulders.
If enemies opposed those earlier monarchs from across so narrow a stretch of ocean, and were able to blockade them by sea whilst others might wall off their peninsula on the landward side, they might bid fair to starve the kings out--as the counts of that castle have done, ever and anon through these five hundred years.
The pure mountain air worked marvels, and, unless complications followed, his cure bid fair to be rapid and lasting.
Hence our guardianships here be lonely, and bid fair to remain so.
By then the wind had dropped and a sunny evening bid fair to usher in good weather for early May, so she did not hurry home and it was getting on for seven o'clock when she got back to the Cromwell Road.
If he was wrong about the magic that moved it, the lives and careers of Craer Delnbone and Hawkril Anharu bid fair to be soon over.