I've made and played several diatonic fretted dulcimer type instruments and when I need a note that's not in that major scale I simply bend the string to get the note just like bending for notes on any other instrument. I'll see if I've got any vids demonstrating this.
Ah, here's one with a little bit of note bending on a diatonic fretted one.
As others have pointed out, Bing Futch is a good resource for playing blues on a dulcimer.
Here is a link to me playing one of his blues songs, it has several bends in it:
Bing sells a Blues 101 book for dulcimers as well.