In 2001, Bloomberg was the Republican nominee and defeated Democrat Herman Badillo.
In 2005, Bloomberg was the Republican nominee and defeated Democrat Fernando Ferrer.
In 2009, although changing his party affiliation from Republican to Independent in 2007, Bloomberg decided to run again as a Republican and was uncontested in the Republican primary. Bloomberg defeated Democrat Bill Thompson.
Doesn’t make him a Republican.
Mark Green was the Democrat that Bloomberg beat in 2001.