This is the perfect answer for you Jagat. Barshaini is the last point till which you have motorable road enroute Kheerganga trek.However, I doubt about parking for your bike, so it would be better to take bus/taxi till Barshaini.
Bro Kheerganga is a trek and you can't motor through it. If you want to avoid trekking and still want to enjoy the top view, go to Parashar lake. From what I've heard, the top can also be reached by car.
Well I suggest prefer public transports to roam around and in this way, you will have the opportunity to interact with local passengers and which led you to better knowledge about the Kheerganga. Maybe they can find you a less-visited more beautiful side of Kasol. Also, I would not recommend going on a solo bike trip at the age of 21(Just a guess). Although you are now legally free to get married :p there is something out there in the wild which you must have to experience with some experienced people first. Good Luck!!
Happy Travelling!!