How long should it take for us to observationally determine if Caltech's Planet Nine is really there? Caltech just released a report that says there is possibly a large (10 earth mass) planet in a remote orbit (10 - 20 thousand year) that explains a lot of observations of Kuiper Belt objects. How long could it take for this to be confirmed or refuted observationally?

See this video
Those are model calculations, which hint to the existence of a possible body of about 10-times the mass of Earth. Calling this a discovery would clearly be premature. The confidence level is just a little above the "evidence" level of 3 sigma, under the assumption, that the discoveries of the KBO objects leading to the inference aren't observationally biased.
It's a long way to direct observation, since precise orbital data haven't been inferred.
Another option is, that there has been a planet. But it might have left our Solar system. Hence predicting a date for direct observation doesn't appear reasonable at the moment.