Bill Cosby -- Backs Out of Next Shows ... On Heels of Gloria Allred's Challenge

Bill Cosby immediately postponed his upcoming live shows ... just minutes after Gloria Allred tried to shame him into putting up $100 mil for his alleged victims.

Cosby was scheduled to do 2 shows in Tarrytown, NY (just N. of NYC) on Saturday -- but about 5 minutes after Gloria's announcement ... the Tarrytown Music Hall said the shows had been delayed.

The venue said Cosby and the promoter reached the decision together ... and everyone will get full refunds. Unclear if the postponement was in direct response to the Allred news conference, but the timing is suspicious.

Several other theaters had already canceled or rescheduled Cosby shows, although his last one in Florida went off without a hitch.