Solution 1:

I agree with mplungjan.

I fixed the bug implies that it was done some time back, and on your own accord, unless you write the sentence as :

After I received the complaint, I fixed the problem...

It also seems like a general statement you are making, maybe in your daily report.

I have fixed the problem, sounds more like you are saying it in response to a complaint/report. It seems to imply :

I have (now) fixed the problem...

Solution 2:

The choice depends on the context, on what went on before in the dialogue and what was likely to follow. As others have said, the past tense implies that the fixing took place some while ago, whereas the present perfect suggests a more recent event and does so in a way that relates it to the current situation.

You don’t ask for comments on the second part of the sentence, but a native speaker would be unlikely to say ‘committed the fix’.