Large aperture towed arrays are widely used underwater to detect weak targets. During maneuvering, the beamformer performance degrades significantly if a wrong array configuration is assumed. Currently, engineering sensors and/or (augmented) acoustic sources are used to estimate the array element positions. The results are often inadequate depending on the number of measurements available. In this paper, an adaptive bow (AB) sparse Bayesian learning (SBL) algorithm is proposed, called ABSBL. Assuming the towed array follows a parabola shape during slow turns and treating the array bow as a hyperparameter in SBL, the bow and directions of arrival (DOAs) of the signals can be jointly estimated from the received acoustic data. Simulations show that ABSBL yields accurate estimates of the bow and target DOAs if the turning direction is known. ABSBL is applied to the MAPEX2000 data. The estimated array bow and DOA agrees with that estimated from relative time delays measured from acoustic pings and SBL, better than that estimated from the GPS data using the water-pulley model. The method can potentially be applied without engineering sensors.