Ajanta

Please forgive my newbie questions but I would appreciate some
guidance.

My family needs to stop in Ankara for a few days en route between India
and USA. Time frame is late December - not good for low fares. :(

A first check with local travel agents shows that Istanbul would be
much more affordable stopover. In that case, what would be the best
options for going to Ankara from there? How long do trains or buses
take and are they safe/comfortable?

Of course it is possible that these agents don't have the right
picture. If Ankara can be inserted in an affordable way, please let me
know.

[Please leave culture.Indian in the group list. That is where I can
most reliably check the replies. Thanks.]