It's dripping because the float isn't floating or the needle and seat isn't sealing. Put your float in a bowl of gas over night and see if it's still floating in the morning. If so replace your needle, that bike has a rubber tip on the needle that gets hard and wont shut off the fuel flow, it's 20 years old.
Get your parts from the Honda dealer. They of course won't have what you need but they can order it.
Try Service Honda's mail order system, it's cheap and just as fast as your dealer.