We propose a technique for synthesizing bidirectional programs from the corresponding unidirectional code plus a few input/output examples. The core ideas are: (1) constructing a sketch using the given unidirectional program as a specification, and (2) filling the sketch in a modular fashion by exploiting the properties of bidirectional programs. These ideas are enabled by our choice of programming language, HOBiT, which is specifically designed to maintain the unidirectional program structure in bidirectional programming, and keep the parts that control bidirectional behavior modular. To evaluate our approach, we implemented it in a tool called Synbit and used it to generate bidirectional programs for intricate microbenchmarks, as well as for a few larger, more realistic problems. We also compared Synbit to a state-of-the-art unidirectional synthesis tool on the task of synthesizing backward computations.