There are few options you can try:
a. Take a car which high clearing like Innova.
b. Take a good motor bike but make sure you are not alone (you may need people to push in case it is stuck, which is very likely)
c. If you have low clearance car and prefer to drive by that, take it till Kodiya village as road is good till there. From there, hire jeep.
2. Irrespective of what mode of transport you are using, have some patience. There are lot of rough patches and water stream where you need to drive carefully and skillfully to make sure you are not stuck and beyond a point, you need to park car/bike and walk. If you try to take it till end, you may be stuck like this Pajero and this is very bad place to get stuck (remember you are in middle of Rajaji National Park which is home to one of the most dangerous elephants in India and kill lot of people every year)