Hello Venuaparna,
Technically, going by what's mentioned in your Confirmation Letter & Bond, the Notice Period CAN go in-parallel.
But, legally, since nothing specific is mentioned in such a situation that you are into right now, the Company CAN take a stand that they HAVE to be IN SERIAL--meaning 1 yr bond + 3 months notice period.
Suggest check out discretely with HR or someone else within the company if there were precedences earlier. If yes, how were they handled. If no, then all I say is that you have to bell the cat & then watch what happens & respond accordingly.
Also, check out with the new company if they will bear the Notice period Buy-out amount.
Looking back, I think you should have done all this thinking BEFORE you even started the process of looking out for better opportunities.
Suggest wait for others to respond also--there could be better suggestions.
Rgds,
TS