Hi ALL, who will stumble on this page with similar problem.
Here is what finally worked.
I contacted support of bluehost, many techy guys, self proclaimed gurus of WordPress etc etc but ALL the advice they gave amounted to Zilch !
” The problem was in the installation of WordPress itself. The simple scripts or fantastico or MOJO please stay away from automatic installs as they just don’t delete the previous databases and overwrite them creating all sorts of funny scenarios where WordPress is left to battle it out with traces/remains of their ancestors while you pull your hair at front end.
SOLUTION : Manually install the WordPress. And before that MANUALLY delete all the old databases and users by accessing them through your file manager provided by respective hosting. I did that and now happily have a https://www.mysite.com/blog
For some this may never become a problem but if it does then the solution is what i have listed above.
Thanks and hope that it helps someone