Mostly what ya need is a good compressor. Use a clean overdrive setting on the amp and set the compression so that it makes all the notes equal in loudness and gives good sustain. Another thing that'll help is to wrap a scrunchie (hairbraid) around the neck so that it dampens any unplayed strings. Learn to use it properly so you can quickly remove it when you want to play open strings.
I've got about 60 pages of tapping lessons on my web page if ya need any more info.