Bilinear restriction estimates which are well known for free waves are extended to adapted spaces $$extract_itex$$V^{2}$$/extract_itex$$ of functions of bounded quadratic variation under quantitative assumption on phase functions. First, we assume transversality, curvature, and regularity condition on phase functions and define atomic Banach spaces $$extract_itex$$U^{p}, V^{p}$$/extract_itex$$, which are introduced by Koch and Tataru. The essence of this talk will follow the argument which shows the sharp bilinear restriction estimates for paraboloid given by Tao. Thus in this talk, wave packet decomposition plays a crucial role.