A Bunny is a cricketer who has been chosen as a specialist wicketkeeper or bowler and has been allocated the No. 11 batting position as he cannot bat. A second meaning of Bunny is a player who is frequently dismissed by a specific bowler.
Some other meanings of a bunny could imply a lower-order batsman who usually struggles to score runs, having been selected in the playing XI as a specialist bowler. One other term which is used to describe a rabbit is 'Ferret', which essentially is even worse than a bunny or a rabbit.
For a batsman who has been frequently dismissed by a bowler, it is also said that the bowler has a 'Hoodoo' on that batsman.
Examples:
New Zealand swing bowler Chris Martin was often called a bunny with the bat given his obvious struggles as a batsman. He finished his career with 123 runs that he scored at a rather underwhelming average of 2.36 in Test matches. He was also dismissed for 36 ducks.
Former England captain Michael Atherton was Aussie fast bowler Glenn McGrath's bunny, having gotten out to him 19 times in 17 Test matches. Similarly Graham Gooch was dismissed 16 times by Malcolm Marshall in Test match cricket and became his bunny.