I am not sure what bleach is going to do to solve the problem. If you think it is a clog, use an enzyme drain cleaner such as Draincare by Zep. Enzyme cleaners are not caustic and will not harm any type drainage system, including septics. Enzyme cleaners cling to, and eat, organic clogs (except tree roots). Caustic cleaners eat a small hole in the clog and then run down the pipes to the sewer system, leaving a partial clog to start the process all over again. Your problem may be venting since you get the burping. Bleach will not hurt the cast iron pipe.
if you have never made a mistake, you probably haven't done much.