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 in right now, the company can take a stand that they have to be in series—meaning 1-year bond + 3 months notice period. Suggest checking discreetly with HR or someone else within the company if there were precedents earlier. If yes, how were they handled? If no, then all I say is that you have to bell the cat and then watch what happens and respond accordingly. Also, check 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 waiting for others to respond also—there could be better suggestions.
Regards, TS