"Kommen Sie ein anderes Mal gerne wieder."
It communicates that the speaker would be happy if the other person comes back another time.
A better translation of the original sentence would be: You're welcome to come back another time. This might reflect 'gerne' better.
Thanks for explaining. I suspected that was the case, but I wasn't sure that the speaker wasn't saying that the other person would be happy to come back, if you see what I mean.
I think it could in principle mean that as well... But it would be such a weird thing to say, so it is clear from the context that this isn't what is meant.
gern and gerne are the same thing. Some people use one instead of the other.