The best way to get there is to hire a car / taxi from Bhopal and drive there. While roads of Madhya Pradesh are not the best, the road leading from the highway upto the Bhimbetka site is great and extremely scenic.
First, there's a railway crossing and on the other side, the road climbs up like a creeper. It is just wide enough for a four wheeler to just fit in.
At the bottom, just at the railway crossing, there is a restaurant but one has to book in advance.