This paper proposes a new joint maximum a posteriori linear regression (MAPLR) adaptation using single prior distribution with a variance function in bilinear transformation space (BITS). There are two indirect adaptation methods based on the linear transformation in BITS and these are tightly coupled by joint MAP-based estimation. The proposed method not only has the scalable parameters but also is based on only one prior distribution, unlike the conventional joint MAP-MAPLR method with two priors. Experimental results, especially for small amount of adaptation data, show the synergy between two indirect BITS-based methods over other methods.