They may be able to predict if it will bend it in such a way as to bring it closer or further away on the next pass, but I don't believe they can make an accurate estimate on the exact distance it will pass next time.
Yes, they can, within an accuracy of plus or minus about 20,000 kilometers. Heck, NASA's already done calculations for not just the next pass, but the next 25 passes going up to 2137
, and you can see for yourself how detailed the calculations are. This is the only pass prior to 2087 when it has any prospect of coming closer to Earth than a hundredth of an AU (1.5 million kilometers).
I can appreciate NASA's ability to create precise estimates on the distances and paths of celestial objects, but I'm mystified as to how they could possibly determine mass. Wouldn't they need to be able to penetrate the object with some kind of sensor to determine density and composition, and in multiple places throughout the object (because density and composition vary from spot to spot)? Not having a precise measurement of mass will skew calculations of gravitational effects, which ultimately affects the trajectory.