The previous record of scoring 28 runs in an over was jointly shared by Brian Lara of the West Indies, George Bailey of Australia and Keshav Maharaj of South Africa, with two of Broad's current England teammates playing an unwanted role.
Bailey hit seamer James Anderson for 28 in Perth in the 2013-14 Ashes, and Maharaj scored his runs against part-time spinner Joe Root in Port Elizabeth in 2020.
Lara hit South Africa spinner Robin Peterson for his 28 in Johannesburg in 2003.
Bumrah finished on 31 not out from 16 balls after India was bowled out for 416.
The 36-year-old Broad ended with 1-89.
Broad was also hit for 36 in a single over in 2007 by India's Yuvraj Singh at the T20 World Cup.