Bonevacia was born in Lelystad and started playing football with VV Reiger Boys in Heerhugowaard, North Holland. Different professional clubs were interested in signing the youngster, including AZ and AFC Ajax, for whom he finally signed his first youth contract in the summer of 2001. Until 2010, Bonevacia played in the Ajax Academy, first as a central defender and later as a defensive midfielder. In July 2008, Bonevacia signed his first professional contract for Ajax, a three-year deal until 2011.
At the beginning of the 2010–11 season, Bonevacia was added to Ajax's senior squad by manager Martin Jol. He made his Eredivisie debut in the starting line-up on 14 August 2010 in a 4–2 victory over Vitesse at the Amsterdam ArenA. His second appearance came on 22 September 2010 in the KNVB Cup where he started and played the full 90 minutes in the 5–0 win against MVV Maastricht at home.
Bonevacia made no further appearances for the first team following the resignation of Martin Jol, and was loaned out to NAC Breda the following season.
In the summer of 2011, Bonevacia was sent on loan to NAC Breda until the end of the season. He played 17 matches in the Eredivisie. At the end of the 2011–12 season, he returned to Ajax, where he attempted to earn a regular place in the first team.
After only making two regular season appearances for Ajax under then coach Martin Jol and making no further appearances during the 2012–13 season, except in pre-season in friendly encounters, Bonevacia was sent on loan to Roda JC Kerkrade until the end of the 2012–13 season. Following his loan spell, Roly Bonevacia signed a two-year contract with Roda JC, binding him to the club from Limburg until the summer of 2015.
On 25 July 2014 Bonevacia signed for New Zealand club Wellington Phoenix in the A-League on a 2-year deal. He re-signed with the Wellington Phoenix until 2016–17 claiming he wouldn't consider leaving until he has won the A-league.
On 16 May 2017 Bonevacia signed for Australia club Western Sydney Wanderers who also play in the A-League on a 2-year deal.
Bonevacia was a member of the Dutch squad at the 2008 UEFA European Under-17 Football Championship, having also represented the U-17 Oranje in the qualification rounds for the tournament.
Since 2009, Bonevacia has represented the Netherlands U-19 team in the qualification rounds for the 2010 UEFA European Under-19 Football Championship. He made his debut for the team in a match against Cyprus, and also played in qualification matches against the Czech Republic and Malta.
In April 2015, Bonevacia expressed a desire to potentially represent Curaçao, the country of his parents' birth. In June 2015, Bonevacia was named to the national squad for a friendly against Trinidad and Tobago and 2018 World Cup qualifiers against Cuba. However, Bonevacia did not appear in any of the three matches, only joined for an unofficial friendly against Suriname in Almere.
PFA A-League Team of the Season: 2015-16