If you happen to forget to reset the axis before fitting the line...
Click the red triangle menu on the linear fit, and then select "set alpha level", 0.05 is the default so click that.
This will redraw the regression line, and it will also redraw the confidence intervals of the individual and fit too.
All you have to do to get the JMP script for this, is to generate the bivariate plot interactively, and then go to the red triangle in the output, and select "Save Script". It will give you your script for reproducing the chart.