You need a bit of choppiness to keep the blues/swing beat--A good trick, which I use on the guitar a lot, is to damp the string (or strings) that I am keeping the shuffle beat on, but letting the others ring--

If you are playing on just one string, you may want to damp it when it is open and let it ring when you play it up the neck--As I think about it, just listen to some good blues slide guitar, and copy--it really doesn't matter how many strings you are playing on--

The most important part is just to have a really funky shuffle feel--