Bicky is Mr. Bickley's dog, given to him by Mork in Season 1's Mork the Tolerant, and who makes several appearances and mentions throughout the show.
About Bicky[]
Bicky was a surprise gift presented to Mr. Bickley by Mork after the Orkan begins to understand that their downstairs neighbor's grouchiness is in large part caused by a lack of someone to care for, and be cared about (Mork the Tolerant).
Mork finds Bicky a new home
Sneaking him into the apartment, he surprises both Bickley and Mindy unveiling the pup from within his jacket. Never having anyone do something like that before, Bickley becomes both emotional and immediately attached to the pup, which he names Bicky.
Bickley's attachment to his new dog in the attention and gifts he lavishes on him (In Mork we Trust), treating him like a child, and confirming to Mork and Mindy that he really does love the pup,
Bicky all grown up
Bicky is seen again, considerably more grown, when he comes up to Mindy's apartment after Bickley, when Bickley comes in search of Mork or Mindy, to borrow the book that Mork was going to lend him. Not realizing that Mork has shrunken down to smaller than mouse sized, Bickley lets his dog wander the apartment, sending a petrified tiny Mork running into a mouse hole to get away from the dog (Mork in Wonderland, Part 1).
While Bicky is not actually seen again, Mr. Bickley continues to talk about him, comparing him far more favorably as a pet to Mork's new caterpillar 'pet', Bob. Then getting highly emotional over his dog in the wake of giving Bob's 'eulogy' and running out of Mindy's apartment back to his own to seek out Bicky (Mork's Best Friend).
While in Alas, Poor Mork, We Knew Him Well, when Mindy concocts the plan to treat a 'retreated' Mork as really gone to get him out of his protective chamber, Bickley confesses to Mork that his plan to take the 'departed' Mork's clothes were only so he could give them to his dog.