Yes, Perl should be sufficiently powerful to output JSON from your format, seeing as you have it in a parsed format already. Convert your bib format into an equivalent of the format the JSON needs to be in and use one of the JSON modules on CPAN to output it, i.e. a hashref like this:

{ name => 'Sigma 1', 
  publication_date => '1997', 
  pages => [ 3, 4 ]
}
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would be return by JSON's to_json function as:

{"publication_date":"1997","name":"Sigma 1","pages":[3,4]}
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For more details on perl data structures (arrays, hashes, arrayrefs, hashrefs) read perldsc.