Again, does "a bad memory" not imply a recollection of a bad thing instead of having difficulty remembering? I'd more likely call the difficulty remembering "having bad memory" while remembering something bad "having a bad memory". Native English seeakers, what do you think?
When talking about memory in general, I would still say "I have a good/bad memory". Oddly, I wouldn't omit the article with "good", but it sounds OK to leave it out with "bad"... maybe that's just me though. When talking about some specific memory, then you would also say "a bad memory" and tell the difference by context, or quite often you would use the plural instead. In most cases you'd say something like "I have a bad memory of..." or more likely "I have bad memories of..."