why would I come back here

In the context of a dialogue like this, both mean the same and both are (probably) equally likely.

Adding "have" is correct, as it refers to a single act in the past, but many would miss it out in informal speech.

1. Which one should I use? WOULD I COME or WOULD I HAVE COME?

2. What's the difference in meaning?

Besides, why would I come back here?

Why would a person [like me] in a situation like this, come back here.

Besides, why would I have come back here?

The focus shifts to "I" and this particular event.

Q: Why would I bother to reply to this posting?

[notice the focus]

A: For the same reason many people do, an interest in language, a desire to help others, mental stimulation, ... .

Q: Why would I have bothered to reply to this posting?

A: Because I have enjoyed helping WB sort out certain issues with respect to modal verbs.

The focus on the 2nd reply was more pointed at the situation but that doesn't mean that every reply has to be that personally focused. 'would' asks/encourages us to speculate, to wonder about possibilities, whereas a "Why did you bother to reply to this posting?" is more direct, more focused, more concerned with facts.

Great advice, McTag, but I don't believe that this is accurate.

Thank you, JTT an Mctag~

"Why would I come back here?" now, or in the future, or anytime.

"Why would I have come back here?"- In the past, once or even multiple times (unlikely to be multiple times; for that, you would probably write something like "why would I have kept coming back here?"

I guess this is as close as you can bring yourself towards honesty.