Well, if I am to be honest, I do not think you'll get there easily on public transport.
My advice, then is as follows: hire a care, preferably with a driver . It will not come expensive, and you can always bargain (but before departure!).
Or you can rely on your skills (no driver to hire in this case) and take a map or GPS!
Freedom is guaranteed in any case!
While walking over and around the ruins of Otrar i noticed great amount of small pieces of ancient ceramics laying in the dust. It was a great fun to search the ground to find a nicer piece than other members of the group. This pieces are fragments of ancient vessles and building decorations. You will not believe it but there is plenty of this stuff even far outside the research area surrounded by fence.
Finally I descided to keep one piece. I think the other guys in the group did the same.
Just don't tell anybody on me, ok?
Fondest memory: It is on the picture