We propose and experimentally demonstrate a compact bending sensor. The head of the sensor is only 0.8 mm in length, and consists of an abrupt biconical fiber taper formed using a conventional fusion splicer, in which a fiber Bragg grating (FBG) is inscribed using a femtosecond laser. The biconical taper incorporating the FBG can couple light from the cladding to the backward-propagating core mode, which realizes an interferometer in reflection-mode. Bending of the structure can be detected from the contrast change of interference fringes. A configuration to measure curvature is investigated to demonstrate the sensing characteristics. The temperature cross-sensitivity of the sensor is studied, and the results demonstrate that it is insensitive to temperature.