HR Not allowing me the release from Notice Period

I had applied for resignation the next day after a planned release with manager in a service based MNC.
I never knew that I need to serve notice period of 3 months even on bench.
I agree that it's more like setting a wrong example. But I can't tolerate the company and it's policies.
Since on bench, I'm having no dependency. I want a release as early as possible.
I'm also ready to buy out the remaining notice period.
HR manager says, she spoke to her senior. If he says yes, then she'll allow. Else I'll be bound to serve the notice period.
I want to join a startup within the next 7 days or I just might lose it.
How to tackle this situation? Am I legally bound to serve the notice period despite being ready to buy it?

You are kept on bench probably due to no work to be allotted with an automatic consequence of less salary. When you have got a better alternative, you are justified to opt for a buy out out of necessity and therefore the management cannot mechanically insist to serve the notice in it's entirety on bench. If don't have any problem with your prospective employer about your formal relief from the present job, pay the notice pay and join the new job. Keep both the employers formally apprised of your decision to do so before hand.