I just constructed the
"super" Joule Thief using the values shown in the video (100pF capacitor, 100kohm resistor) from some parts around the house and a ferrite core (the ring shaped thing in the video) I pulled out of some old electronics. I just wound some random number (maybe 15 or so) of turns around the ferrite. It was able to power at least 7 UV diodes I had on hand in parallel from one 1.5V battery. I didn't tune it and I used some cheap wire from an ethernet cable, but it still worked.
You can probably get similar or better results as well, and adding turns to the ferrite usually improves the brightness. I'll see if I can come up with a parts list from Mouser.com (an online electronics part store) if you want to build it. The total cost would probably be about $5 (~$2 for the ferrite, $0.30-$0.70 for each transistor, $0.60 for the cap and resistor, $1 for a battery holder), though maybe more from the cost of the protoboard to solder the parts from. We can draw what the parts look like and how they'd be connected if you can't read schematics.
Regardless of whether you want to build a JT or not, you'll probably want to buy a real battery holder from an electronics part shop. Better than fussing around with a makeshift holder, especially if you need to swap batteries.
On another note, I compared the brightness of those UV LEDs to a white LED. The UV LEDs looked so dim, so I thought maybe they weren't getting enough current. Well, the white LED is just as bright as ever, so it's really the UV LEDs that are very dim. I don't know how much mileage you'll get from them even at full power as a blacklight source.
I still suggest you consider buying a 6-inch 4W compact fluorescent black lamp rather than go with LEDs. You can strap it to your back and have it flood light outwards. The fluorescent lights put out about 0.5W worth of UV from the fluorescent black lamp; compare that with maybe 5mW per LED--if that--and you'd need a hundred LEDs to even approach the brightness of a single portable lamp. They're only
$7 each (
alternative). You can still use (and should) regular LEDs (like blue or white) to decorate the tutu, but if you're really looking to "glow" you really need something like the fluorescent light.