Along with others, I agree both OP's sentences are "valid", but neither existing answer seems to address the issue of whether either is "preferred". The mention of "perfect tense" in the title is irrelevant - usage is unaffected by "has been/has had" (present perfect) or "was/had" (simple past).
The issue under consideration is just "had" vs "was a good/bad influence". From Google Books:
- "he had a bad influence on me" - 5 instances.
- "I had a bad influence on her" - 1 instance.
- "she had a good influence on him" - 6 instances.
- "he was a bad influence on me" - 392 instances.
- "I was a bad influence on her" - 1120 instances.
- "she was a good influence on him" - 131 instances.
I think that's enough to establish that if we're talking about "influence" as something that causes positive/negative changes in the person being influenced, we normally speak of being an influence.
It's different if we're talking about "influence" where the moral development of the influenced party isn't central - for example, trying to persuade someone to do something. There, constructions like "he has influence with/over them" dominate. All variations of "he was an influence/influential with/over them" are either unusual or unknown.
TL;DR: You are an influence on [the moral development of] others (it's an ongoing state). Whereas more commonly you have influence you bring to bear on specific occasions, to persuade someone to adopt a particular course of action.