Thanks for the great question Belinda! Personally I would say it should take students between 2-3 months of solid practice to get it down. I always compare this to someone that wants to become a body-builder. No matter how hard you try, you couldn’t become a body-builder with a few good sessions in the gym–it would take many months and even years! Fortunately development of vibrato doesn’t take as long, but the concept is the same. You have to develop muscle memory which takes 2-3 months of good solid repetition.
If you haven’t had a chance to check out my vibrato article, I would highly recommend it. Notice a link at the bottom which will forward you to forum thread that has some really good video links on it related to the process.