I have been arguing with friends on this. Is it right to say 'go by a bus' or 'go on a bus'?
Either are quite understandable, and even grammatical.
Idiomatically one would usually say I shall go by bus (the indefinite article is out of place in this context).
In some situations if you wanted to stress that you were going by bus, as opposed to walking or some other transport mode, it might be appropriate to say I shall go on a bus (indef. article essential).