I met my current partners mum about a month in.. partner met my dad within think about a week but that was because dad wasnt well etc so we went up there..
When ever you feel comfortable to do so both of you really.
The right time depends on your mood. I met mine when I was kinda grumpy and tense due to some problems at work and it didn't go very well. I think the best time is when you are relaxed and fun.
as a mum with two sons, I would suggest the best time is when you are quite committed and you think its going to be pretty long term. I have met several of one of my sons partners, but non of the other ones as he is still of the mind that there is not a need until he feels its the right one, which I must admit I prefer....and he is the most sensible one of the two!! Anyway good luck when u do.