We investigate the self-interference characterization, achievable rate, signal detection and parameter estimation for bi-directional ultra-violet (UV) communication. We firstly characterize and experimentally demonstrate the self-interference of UV communication, which is non-negligible as the angle between the transmission and receiver directions is blow 60°. Then, we present the achievable rate and symbol detection under self-interference, which show that the offset between self-interference and desirable symbols can increase the achievable rate and decrease the symbol detection error probability. We propose the practical system design with parameter estimation under self-interference. Finally, we experimentally evaluate the receiver-side signal detection with self-interference generated by Field Programmable Gate Array, and the signal detection of a real bidirectional UV communication system. Lower symbol detection error probability can also be observed as the offset between desirable symbols and self-interference symbols increases to half-symbol length from both system-level simulation and real experiments, which further validates the theoretical results.