score:5
There is little public transport in Mongolia, particularly if you want to visit the countryside.
You can rent your own car, but that will be expensive. Plus, what happens when your car breaks down in the middle of nowhere? How are you going to make sure you always have enough gas?
I think your best bet is to go on an arranged tour, like the one you did, but with a small group. That way, the overhead is shared and the cost per person should be less. And, book in-country, not while abroad. Doing this would also significantly lower the price.
(Or, consider this. I met the guy when I lived in Mongolia. He mostly traveled by horse.)