Your question actually boils down to choosing between the present tense—“I have experience in bartending”—and the past tense—“‘I had experience in bartending”—when talking about one’s work experience.
Recall that “have” is a present-tense transitive verb that means to obtain or be in the possession of something. Thus, the sentence “I have experience in bartending” conveys the idea that the speaker acquired the experience at some time in the past and continues to be able to do bartending up to the time of speaking. In other words, the state of having that bartending experience hasn’t ended but persists up to the present, so the speaker is confident of putting that experience to good use up to now.
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In contrast, “had” as the past tense of the transitive verb “have” conveys the sense of having obtained or having gotten possession of something in the past without necessarily retaining it. Thus, the sentence “I had experience in bartending” conveys the idea that although the speaker did get the experience of bartending at some time in the past, he or she might have lost the skill or knack for it so is no longer very confident of being able to put that bartending experience to good use now.
As implied in your observations, there is therefore a semantic wrinkle when one says “I had experience in bartending.” It actually belittles the value of the work experience being invoked by the speaker, and is almost like saying “I experienced bartending but it didn’t amount to much.” This is obviously not the sense that an applicant would want to convey during a job interview.
You are therefore absolutely right that “I have experience in bartending” or ‘I have bartending experience”—both present tense forms—is the grammatically and semantically correct statement to use in this particular situation. Saying it will give assurance to the interviewer that the applicant still possesses that skill and, this being the case, should be seriously considered for the job at hand.