I had an job interview today that went well and I accepted the job offer. The interview was in the morning during work hours so I had to make an excuse about why I was late coming into my current job. I just said that there was an issue with my car. I said this because I know that you shouldn't tell that you are interviewing somewhere else and I didn't know what else to say about why I was late.
Anyways, that is in the past, and now I am wondering, since I am usually very punctual, and I accepted the job on the day I was late, people will naturally assume that I was lying and that I was late because of the job interview. Now what I want to know is if someone asks if I was late because of the interview, should I continue the lie and say that my car was really out of order, or should I come clean and be honest?
I feel like either option has the potential of burning bridges. I will immediately burn bridges if I say right away that I lied. But I could burn bridges in the future if they later find out themselves that I went for an interview at that time.