How strong of a grasp do you need?
Simple conversational is doable in 1 year at a University setting.
I'm a native speaker. I took Intro to Chinese for native speakers (1 year of content for non-speakers done in 1 semester) and 2nd year Chinese. I don't really know, but I think after the 2nd year, most people would be able to travel with the help of a pocket dictionary.
Of course, this is 3 times a week with homework, so if your class is less rigorous, you might not be learning as quickly.