Bradshaw grew up in Stokes Valley and was a promising rugby union player. He was noticed for his basketball talent at St. Bernard's College in Lower Hutt and spent his last two years of high school at Wellington High School, where he focused solely on basketball. In 2002 and 2003, he played in the New Zealand NBL for the Wellington Saints. In 13 games for the Saints over two seasons, he averaged 3.8 points and 2.8 rebounds per game.
Bradshaw played four seasons of college basketball for Winthrop University in the United States between 2003 and 2007, where he averaged 9.2 points and 4.7 rebounds in 123 games (104 starts). During that time, the Eagles played in three NCAA Tournaments and won three Big South Conference championships. As a junior and senior, he was named to the Big South Conference All-Tournament Team, while also earning Tournament MVP and first-team All-Big South as a senior.
After going undrafted in the 2007 NBA draft, Bradshaw joined the Atlanta Hawks for the NBA Summer League tournament in Salt Lake City. In five games for the Hawks, he averaged 4.4 points and 1.8 rebounds in 10.0 minutes per game.
Following his stint with the Atlanta Hawks, Bradshaw joined the Brisbane Bullets for the 2007–08 NBL season. In 30 games for the Bullets, he averaged 13.5 points and 5.7 rebounds per game.
In March 2008, Bradshaw signed with Turkish team Efes Pilsen for the rest of the season. In six games for Efes, he averaged 6.2 points and 3.3 rebounds in 15.8 minutes per game.
In August 2008, Bradshaw signed with Spanish team Grupo Begar León. In 34 games for León in 2008–09, he averaged 9.4 points and 5.1 rebounds per game.
In August 2009, Bradshaw joined Korean team Changwon LG Sakers. In December 2009, he left Changwon and returned to Australia, signing with the Gold Coast Blaze as an injury replacement for Pero Cameron. He spent the remainder of the 2009–10 NBL season with the Blaze, helping them reach the semi-finals where they were swept 2–0 by the Perth Wildcats.
On 12 March 2010, Bradshaw signed with Latvian team VEF Rīga. However, on 3 May 2010, he parted ways with Rīga after sustaining a season-ending leg injury.
On 23 December 2010, Bradshaw with the Otago Nuggets for the 2011 New Zealand NBL season, returning to the league for the first time since 2003. He appeared in all 16 games for the Nuggets in 2011, averaging 18.5 points, 8.5 rebounds and 2.4 assists per game.
On 28 October 2011, Bradshaw signed with the Southland Sharks for the 2012 New Zealand NBL season. He appeared in all 16 games for the Sharks in 2012, averaging 17.1 points, 5.4 rebounds and 1.1 assists per game.
Bradshaw represented New Zealand with the Tall Blacks at the 2004 Summer Olympics, 2005 FIBA Oceania Championship, 2006 FIBA World Championship, 2007 FIBA Oceania Championship, 2008 Summer Olympics, and the 2010 FIBA World Championship. Bradshaw put his name up in bright lights in 2006 when he scored 25 points to help lead the Tall Blacks to their first away win over Australia.
In 2012, Bradshaw married Felicity Kenny. The couple have one daughter together.
Bradshaw has an entrepreneurship degree and set up his own travel management company, New Zealand Specialty Tours, which specialises in developing custom-built itineraries for visitors to New Zealand.
In October 2016, Bradshaw was ordered to pay a $750 emotional harm fee after he was convicted of kicking a bouncer in the head at a Queenstown bar on June 13, 2014. He was sentenced on one charge of assault with intent to injure and, as well as the emotional harm payment, was ordered to pay a $500 fine along with courts costs. In March 2017, he had an appeal against his assault conviction thrown out. Bradshaw appealed against a conviction of assault with intent to injure, based on "undue delay" in the court process, errors in the way the trial proceeded and the refusal of a discharge without conviction.