Yes, you need grooves in the bridge for the strings to ride in.  Grooves hold the strings in the proper spacing, preventing them from wandering all over the top edge of the bridge.  The grooves must be of the proper shape and depth to give support to the strings and keep them from sticking or buzzing in the slots. You might want to get an experienced luthier to do the job.

p.s. Grooves In The Bridge sounds like a good fiddle tune name.

--
Site Owner

Those irritated by grain of sand best avoid beach.
-Strumelia proverb c.1990

Are there string grooves in the nut?
Yes i would venture to say there should be some grooves in the bridge, to hold the string spacing even despite any vigorous strumming or plucking at that end.

If you could attach a photo here it would be additionally helpful.  :)

--
Site Owner

Those irritated by grain of sand best avoid beach.
-Strumelia proverb c.1990
updated by @strumelia: 06/28/25 10:10:49PM

Okay, different dulcimer, new question. I pcked up a Folkcraft dulcimer off Ebay. I think the strings were the originals from 1987. I have replaced the strings now but noticed that the bridge is completely smooth on both sides. My other dulcimers have a groove of some sort on both the nut and bridge.  Do I need grooves on the bridge?  Not sure yet how I feel about this dulcimer.