Hello Siddy,
Come to the USA and join the fun in a motorhome. Think about flying into Seattle (SEATAC) airport and renting there. Several rental options are available as mentioned above. From there it is about 500 miles or so to Yellowstone.
While in the Seattle area, consider a trip to the Hoh rain forest in western Washington. Go to Port Angeles, then Forks (all about the Twilight books), then on to the rain forest. This would give you time to familiarize yourself with our style of RV's. We live in Port Angeles and often help folks with rentals that were not introduced properly to the RV setup and so on.
We also have several folks living here in town from Britain who came to visit and stayed.
Keith