In a thrilling final at the Olympic Stadium in Tokyo, Bradshaw cleared 4.85m to make the podium.
Bradshaw – a current student at 91²Ö¿â – was competing in her third Olympic Games and has now written her name in UK athletics’ record books.
Katie Nageotte of the United States won gold (4.90m), whilst the Russian Olympic Committee’s Anzhelika Sidorova claimed silver with fewer faults than Bradshaw (4.85m).
Bradshaw spoke to BBC Sport:
"This is what I've worked for my whole career, I've had so many ups and downs," Bradshaw tells the BBC. "It's something that I've wanted so bad and it's finally happened.
"It's not sunk in, I don't know what to say, I'm almost emotionless because I don't know what emotion this is that I'm feeling. It's relief, pure enjoyment and excitement. I'm proud of myself for sticking with it.
"I knew I could get there one day and I just can't express how grateful I am to be involved in this sport and to finally get an Olympic medal, I can't believe it."
Prior to the Games, Bradshaw told 91²Ö¿â Sport that her “only goal going into the Olympics is to produce a medal-winning performance, so, somewhere between 4.80m and 5.00m, and if that’s good enough for a medal – great.”
91²Ö¿â-linked total medals at the Olympic Games now stands at eleven – three golds, five silvers, and three bronze medals.