In this paper, we propose a context adaptive bit-plane coding (CABIC) with a stochastic bit reshuffling (SBR) scheme to deliver higher coding efficiency and better subjective quality for fine granular scalable (FGS) video coding. Traditional bit-plane coding in FGS algorithm suffers from poor coding efficiency and subjective quality. To improve coding efficiency, our CABIC constructs context models based on both the energy distribution in a block and the spatial correlations in the adjacent blocks. Moreover, it exploits the context across bit-planes to save side information. To improve subjective quality, our SBR reorders the coefficient bits by their estimated rate-distortion performance. Particularly, we model transform coefficients with Laplacian distributions and incorporate them into the context probability models for content-aware parameter estimation. Moreover, our SBR is implemented with a dynamic priority management that uses a low-complexity dynamic memory organization. Experimental results show that our CABIC improves the PSNR by 0.5-1.0 dB at medium and high bit rates. While maintaining similar or even higher coding efficiency, our SBR improves the subjective quality.