Bitcoins cannot be "transferred" to any fiat currency or any bank account. If you need to liquidify your bitcoins and you want to get fiat currency in exchange, you can sell your bitcoins in Bitcoin exchanges. Alternative is that you directly spend bitcoins on bought products and services.
If you just want to store your bitcoins you can create your own local Bitcoin wallet independent of online bitcoin services.
No financial institution will touch bitcoins. In fact, most banks and PayPal are openly hostile towards anything having word "bitcoin" on it.
Good options to sell your bitcoins in India is LocalBitcoins where you can sell bitcoins online, or on the street with cash. Be aware that there are some risks, and those risks are especially when selling bitcoins on PayPal. Unless you are professional you should not be doing Bitcoin sells on PayPal.
What I would do is that I would transfer my bitcoins to LocalBitcoins trade wallet, pick a trader with high reputation (so him/her can be trusted) from LocalBitcoins "Sell bitcoins online" list and make an offer to sell my bitcoins using Indian bank transfer.