According to Waugh, Marcus Harris and veteran Shaun Marsh should open the batting, followed by incumbent Usman Khawaja.
Bumrah, who played a stellar role with match haul of nine for 86 in India's 137-run win against Australia at the MCG, has played nine away Test matches this year with 48 wickets in this current calendar year.
Wade, who has scored 886 runs in 22 Tests, last wore the Baggy Green in September 2017 when Australia were on tour to Bangladesh.
Warne was stunned with the numbers which showed only Cummins, with 30 wickets at 23, was averaging below 30 against the top-six batsmen.
Bumrah, who claimed 9/86 in the MCG Test, has achieved the best match figures by any Indian pacer in Tests in Australia.
This is the first time that India have won the Boxing Day Test in Melbourne and the first time since 1981 that they have won a match at the MCG.
Paine admitted that his batsmen failed to cope with the high-quality opposition bowling attack in the absence of banned Steve Smith and David Warner.
After India declared at 443/7 in their first innings, Australia could only manage 151 runs in 66.5 overs.
Kohli believes the win has given them the belief that they can put the finishing touches at the SCG.
India needed just 5.3 overs to bowl out Australia for 261, claiming the match by 137 runs and take a 2-1 series lead.