A former West Indies under-19s captain, Bradshaw's senior debut came two months before his 30th birthday, when he was selected to play in the last three One Day Internationals of a seven-match series against England. After taking five wickets in the three matches, he became a permanent fixture in the team. In September 2004, Bradshaw was a member of the West Indies team that won the 2004 Champions Trophy, and was named man of the match in the final. He made his Test debut in March 2006, taking three wickets in each innings against New Zealand, and played five matches before being dropped.
Bradshaw captained West Indies under-19s during their tour of England in 1993, playing three youth Tests and two One-day Internationals. However, as he failed to impress the national selectors of Barbados enough to get first class time for Barbados before January 1998, he was also out of the regional selectors' thoughts, even though he captained Barbados from 2000–01 onwards.
In January 2004, Bradshaw was named in West Indies' 15-man ODI squad which played South Africa, as "reward for good performances during the Red Stripe Bowl", where Bradshaw had taken five wickets for 22 runs to be named Man of the Match in the semi-final. However, Bradshaw did not play a single match, returning to Carib Beer Cup cricket to take six wickets in the Carib Beer Challenge final, where Barbados beat Jamaica.
He was given another ODI selection in April 2004, against England in a 7-match series, but Bradshaw was not selected for the first four games, before taking two wickets as West Indies won the fifth match of the series by five wickets on debut at Beausejour Stadium. Bradshaw ended with five wickets for the series, and his economy rate of 5.50 is still the highest of his career to date.
Bradshaw was retained for the three-match series with Bangladesh, winning the Man of the Match award after bowling figures of 10–4–11–2, the most economical of his ODI career, and an unbeaten 12 as West Indies won by one wicket. He ended with five wickets at a bowling average of 9.60 for the series, thus ending third in the wicket-taking tally for the series behind Tino Best and Tapash Baisya.
West Indies played 11 ODIs in England in 2004, and Bradshaw played in every single one save for a rained off match at Southampton against New Zealand. The first seven matches were during the NatWest Series, where West Indies finished second after losing the final by 107 runs. Bradshaw opened with no wickets in a no result against New Zealand, then removed both England openers with his first seven balls at Trent Bridge in a seven-wicket win, before failing to take a wicket through the 32 overs in the remaining four matches. Bradshaw's bowling average of 85.50 was the highest by any West Indian in the series, but his economy rate of 3.71 was the best by a West Indian, and only beaten by Chris Cairns among bowlers with more than 10 overs in the tournament.
Bradshaw was retained for the 2004 Champions Trophy, taking three wickets in the opening group, which West Indies won by beating Bangladesh and South Africa. He also removed Salman Butt for a two-ball duck in the seven-wicket semi-final win over Pakistan. However, it was in the final that he, along with wicket-keeper Courtney Browne, made headlines West Indies had bowled England out for 217, with Bradshaw taking the wickets of Vikram Solanki and Michael Vaughan, but conceding the most runs of all West Indian bowlers with 54. With more than 15 overs left, Bradshaw joined Courtney Browne at the crease, with West Indies at 147 for eight and needing nearly half that score, 71, from the two last partnerships to win the game and the Champions Trophy. Bradshaw and Browne saw off the England fast bowlers of Steve Harmison, Andrew Flintoff, and Darren Gough in "dubious light", knocking off the required runs with seven balls to spare, thus giving West Indies their first major one-day title since the 1979 World Cup. Bradshaw's 34 not out along with his two wickets, made him Man of the Match, despite partner Browne making one more run and Wavell Hinds taking one more wicket with three for 24.
After playing for Barbados in the 2004–05 Regional One-Day Competition, Bradshaw was selected for the VB Series in Australia. Though Bradshaw was the leading wicket-taker for West Indies, with nine wickets in six games, including three wickets in the final group stage game against Pakistan when a win would have seen the West Indies through to the final stages. However, though Bradshaw took three for 47 from his ten overs, Pakistan totalled 307 for eight, and Bradshaw was called in to bat with 51 required off 37 balls. His innings was not a repeat of the Champions Trophy effort, however, as he was bowled by Naved-ul-Hasan for a four-ball duck; West Indies lost by 30 runs as they were bowled out with eleven balls to spare. During the series, Bradshaw injured his heel and was out of cricket for a fortnight, missing Carib Beer Series matches in domestic cricket.
Bradshaw continued to be an ODI specialist, playing all eight home ODIs (five against South Africa and three against Pakistan) during May 2005, and being on the losing side in all eight. His best performance in terms of bowling figures came in the rain-shortened second ODI at Sabina Park, where Bradshaw removed Graeme Smith and Jacques Kallis in his first three overs, and ended up with conceding 16 runs in six overs. However, no other West Indies bowler took wickets, leading to an eight-wicket defeat.
Bradshaw was then selected for the 13-man Test squad to face Pakistan, and was "expected to make his Test debut", but suffered a viral infection and missed the first Test before being selected in the squad for the second match. However, despite West Indies going in with four seam bowlers, they left Bradshaw out of the team.
A contract squabble between the West Indies Players' Association and the West Indies Cricket Board meant that several players, including Bradshaw, refused to sign contracts for the 2005 tour of Sri Lanka, and Bradshaw did thus not feature in the Indian Oil Cup ODI tournament during this tour.
He thus got a break from international cricket until February 2006, as West Indies' November 2005 tour of Australia only included Tests. Bradshaw played all matches on the February and March tour of New Zealand, however: one Twenty20 International, where he bowled the final over with New Zealand requiring 17 to win, conceding 16 to set up a bowl-out, five ODIs, and three Tests. Once again, Bradshaw was West Indies' leading wicket-taker in the ODI series, this time shared with Dwayne Smith, but with a better economy rate than Smith. His rate of 5.27, however, was bettered by six New Zealand bowlers as New Zealand won the series 4–1.
Bradshaw then made his Test debut at Eden Park, taking six wickets for 156 runs in the match, the second best bowling figures behind Chris Gayle, but New Zealand still prevailed by 27 runs after West Indies lost their way from 148 for nought to 263 all out, Bradshaw making 10 in an hour-long innings that was ended by him giving a catch to Stephen Fleming off Daniel Vettori. In the following two matches, Bradshaw took one wicket, though West Indies did not bowl in the final match, which was affected by rain. The returns were, however, good enough for the West Indies selectors to retain him for the home Test series against India, though in the meantime Bradshaw had taken nine wickets in the first four ODIs against India, helping West Indies to a 4–1 win. Bradshaw was not in the XI for the final game, but still held a catch as substitute fielder. Bradshaw then featured in the first two Tests against India, recording two wickets for 271 in two drawn games. Brian Lara, however, said Bradshaw "[had] been good" during the series in the aftermath of the third Test at St Kitts, where Bradshaw had been left out in favour of an extra batsman.
Bradshaw was selected in the West Indies squad for the 2007 Cricket World Cup. However, he only played in 3 matches with the West Indies generally preferring to use Daren Powell, Jerome Taylor and Corey Collymore as their pace bowling attack. After the West Indies' elimination from the tournament, Bradshaw retired from international cricket.