After joining local side Yeovil Town at the age of nine, Bleazard eventually moved on to FA Women's Premier League club Bristol City at the end of season 2004–05.

[3] At the FA Women's Cup final at the Ricoh Arena in May 2011 Bleazard struck the crossbar with a free kick, but Bristol were beaten 2–0 by Arsenal.

After two seasons with Chelsea, Bleazard agreed a deal to return to Yeovil, whose application to the new second level of an enlarged WSL has been successful.

[9] Bleazard later switched her footballing allegiance to Wales and was named on the standby list for their March 2011 Algarve Cup campaign.

[10] Bristol Academy teammates Jessica Fishlock and Alex Culvin joked that Bleazard's eligibility for the Welsh national team arose from "her Nan's Sister's Brother's Aunty.