Actually the main highway in eastern Russia is all paved by now. The truckers I met called it "Putin's Highway", since he made it a national goal to pave a route from Moscow to Vladivostok. No small feat either. In much of Siberia, the soil turns to bog in the summer when the upper permafrost melts, so the roadway is built up on a high mound so it stays "high and dry".
I'm not sure I would take a bus on a trip like the one I took in 2010-2011. Part, if not most, of the pleasure came from being in touch with the locals, camping in their fields, cooking over a campfire at the end of the day or deciphering (or not!) the menu in a roadside cafe. Being in a bus, I would have missed out on so much. And the border crossings would have been a nightmare. Border officials look at a motorcycle and know the rider is likely not smuggling contraband. But a bus? A search could be an all-day affair.
And after doing a quick calculation, I would have spent 100% of my budget on fuel alone!
Oh, and I wouldn't take a school bus into Mongolia. Maybe the paved road from the border crossing south of Ulan Ude to the capital Ulaan Baatar, but off into the wilderness....no way.