I use alligator clip lead wire as my bridgewire. Alligator clip wires have many strands of very fine wire, so a single strand works well for the bridgewire. Larger diameter wires can carry more current with less resistance, so they don't explode as well. I usually crimp larger wires to the ends of the bridgewire; these serve as long leads for the detonator. When the wire is connected, I tape the thicker leads a distance apart so they don't short.
The power supply for an EBW is a capacitor. I asked Walgreens for used-up disposable cameras, and they gave me five of them. I removed the flash capacitors from them and soldered them in parallel, making sure to connect all the white (-) sides together. I zapped myself a few times desoldering the capacitors, and while it is OK to be haphazard with single capacitors, the five-capacitor bank could possibly kill someone if used improperly. Be careful with large capacitor banks.
This homemade EBW has many uses. I have used it many times to ignite nitrocellulose, sometimes with highly explosive results. EBWs are also good for making loud noises, so wear hearing protection. These devices are very fun and simple to build, even if not used for high explosives.