Why did Shakespeare write 'Exit pursued by a bear.'

In the later 16th Century in Shakespeare's England, the bear pits were an adjunct, not a cheap alternative to the playhouses.

On Thursdays and Sundays of each week , the theatres were closed and the adjoining bear pits opened. One of the 'sports' on such nights was to taunt a blind bear by men with whips, it was not unknown for the maddened bear to break loose form its chains and run among the crowd.
Hence in The Winter's Tale  the stage direction Exit Pursued by a Bear.