Epidural electrostimulation has shown promise for spinal cord injury therapy. However, finding effective stimuli on the multi-electrode stimulating arrays employed requires a laborious manual search of a vast space for each patient. Widespread clinical application of these techniques would be greatly facilitated by an autonomous, algorithmic system which choses stimuli to simultaneously deliver effective therapy and explore this space. We propose a method based on GP-BUCB, a Gaussian process bandit algorithm. In n = 4 spinally transected rats, we implant epidural electrode arrays and examine the algorithm's performance in selecting bipolar stimuli to elicit specified muscle responses. These responses are compared with temporally interleaved intra-animal stimulus selections by a human expert. GP-BUCB successfully controlled the spinal electrostimulation preparation in 37 testing sessions, selecting 670 stimuli. These sessions included sustained autonomous operations (ten-session duration). Delivered performance with respect to the specified metric was as good as or better than that of the human expert. Despite receiving no information as to anatomically likely locations of effective stimuli, GP-BUCB also consistently discovered such a pattern. Further, GP-BUCB was able to extrapolate from previous sessions' results to make predictions about performance in new testing sessions, while remaining sufficiently flexible to capture temporal variability. These results provide validation for applying automated stimulus selection methods to the problem of spinal cord injury therapy.