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Bumrah overtook Kagiso Rabada and Josh Hazlewood for top spot in ICC bowlers rankings.
The 22-year-old scored a brilliant 161 in India's 295-run win over Australia in Perth.
Jaiswal made 161, his first Test century in Australia, while Kohli hit 100 as India declared at 487/6.
The 50-run mark was breached in a mere three overs against Bangladesh on the fourth day of the Kanpur Test.
Indian skipper Rohit Sharma has dropped a spot to sixth.
Sai Sudharsan, Jitesh Sharma and Harshit Rana have been named as replacements.
Jaiswal was Indian captain Rohit Sharma's opening partner in the home T20 series against Afghanistan earlier this year but his place looked under threat as he struggled for runs in the IPL -- 39 being his highest score in his first seven matches.
RR continue to top the table with 14 points from eight games, while MI are struggling in seventh place with six points from eight outings.
Jaiswal ended the series with 712 runs, including two double hundreds and three fifties at an averaging 89 and a strike rate of close to 80.
Jaiswal became only the second Indian after Gavaskar to tally over 700-runs in a Test series.
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