For effective display of fluorescent minerals, you will need darkness and a nonfluorescent setting.
For showing them at home, darkness is easily obtained. But gem & mineral shows and such generally do not allow you to shut off the lights. Short of setting up a tent in the exhibit hall, or getting space in an adjoining room where lights can be turned off, you need a mostly opaque box with some sort of viewing port. It helps the exhibit if the viewer can see the minerals under shortwave UV, longwave UV, and visible light in turn. This can be done with a timer that turns on first one then another lamp, or by providing switches or buttons for the viewer to select lamps with.
For public or prolonged displays, the person viewing the display should be protected from shortwave UV. Ordinary types of glass will stop shortwave UV almost completely, so placing glass between specimen and viewer (not between specimen and lamp!) should be sufficient. Take notice of which side of the glass is fluorescent and face it away from the UV light when shortwave UV is used.
A nonfluorescent background (including labels) is also needed to avoid 'competition' for the mineral fluorescence. Bleached or brightly colored fabrics and papers, many plastics, and even some woods will fluoresce. Black things (including minerals) rarely fluoresce; dull black fabric or paper, or wood painted dull black will generally be best. Black is also good at minimizing the effects of any stray visible light that leaks in.
The white rectangular cardboard jewelry boxes with cotton that often come with bought specimens are usually fluorescent (both box and cotton). Try spray-painting the boxes black and wrapping the cotton in a piece of black cloth. These in turn are kept in black-painted flat boxes. This allows one to simply open the flat box and shine a UV lamp on the specimens.