The South African-born New Zealand batter achieved the feat while playing for Canterbury against Otago in the Ford Trophy, thus breaking the record for the fastest double century in the 50-over format.
Eventually, Bowes was dismissed for 205 off 110 deliveries.
Jagadeesan and Head had reached their respective double hundreds in 114 balls.
Head achieved the feat for South Australia against Queensland in the 2021-22 Marsh Cup, while Tamil Nadu's Jagadeesan did it during his record-breaking 277 against Arunachal Pradesh in the 2022 Vijay Hazare Trophy.
Bowes, who created the record right after missing out on making it to New Zealand's white-ball tour of Sri Lanka, raced to his century in 53 balls and fell short by four balls to match Ross Taylor's record (off 49 balls) for fastest hundred in the competition.
Bowes got to his half-century in 26 balls.
Playing his 100th List A match, Bowes smashed 27 fours and seven sixes as he powered Canterbury to 343 for 9 after they were put in to bat at the Hagley Oval in Christchurch. Canterbury then bowled out Otago for 103 to register a massive 240-run win.
The 32-year-old Bowes, who was born in Benoni, South Africa also became the first player since Jamie How to score a double century in the tournament's history. How scored 222 for Central Stags in the 2012/13 edition of the tournament.
This was Bowes' highest List A score, easily going past his previous best of 126. Known for his swashbuckling batting at the top of the order, he has also appeared in a few ODIs and T20 Internationals for New Zealand in the past.