Didn't quite understand your question and mostly the bitmap part.
Maybe this helps - if you index those JSONs as events, and then have your events with parameters k1,k2,k3... you can use this easy stats/timechart trick:
... | stats count (k*) as k*
and the timechart one -
... | timechart count (k*) as k*
you will get a count for each field starting with K, overall or over time.
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