I suppose they may have only been involved since 2009, however the Foundation has already contributed $1.2 billion with another 1.8 billion on the way.
Of course, as you mentioned, much credit goes to "various governments, the WHO, Rotary International, the U.S. Centers for Disease Control and Prevention and Unicef."
The work done by the Gates foundation is admirable. But the $1.2 billion was donated to the Rotary International for the Global Polio Eradication initiative, not exclusively to be used in India. In fact, it's not even clear if any of that was used in India at all. Moreover India itself has donated $1.3 billion for the Global Polio Eradication initiative.
The Gates foundation offered a $100 million matching grant to Rotary International's Polio Plus program in 2009. The intial matching grant and subsequent increases have been matched by Rotary's members.
Of course, as you mentioned, much credit goes to "various governments, the WHO, Rotary International, the U.S. Centers for Disease Control and Prevention and Unicef."