You can do this in JMP 11 with Graph Builder. Prior to version 11 you could only label bars using the Chart platform.
Here's an example that displays the bar label in JMP 11:
dt = open("$sample_data\Bands Data.jmp");
dt << Graph Builder(
Show Control Panel( 0 ),
Variables( X( :ink type ), Y( :viscosity ), Overlay( :cylinder size ) ),
Elements( Bar( X, Y, Legend( 2 ), Bar Style( "Side by side" ),
Summary Statistic( "Mean" ), Label( "Value" )
)
)
);
In Graph Builder you use the label combobox to select Value: