Combine butter, corn syrup, and salt. Add sugar and mix until smooth. This makes a fondant. Chill in refrigerator for 1/2 hour.
Drain cherries and let dry on paper towels.
Flatten a small amount of fondant in your hand and wrap around a cherry (completely cover the cherry or juice will leak out and make dipping difficult). Repeat with remaining fondant and cherries. Refrigerate fondant-covered cherries and let harden.
Melt chocolate in double boiler or microwave. (To melt in microwave: In microwave-safe bowl, heat chocolate in batches on 50% power for 2 minutes. If not melted, continue to heat for 30-second intervals. It won't look completely melted. Stir until smooth.)
Dip fondant-wrapped cherries into melted chocolate. Coat completely. (Gently reheat chocolate as necessary if it thickens too much while dipping.)
Set on cookie sheet lined with parchment paper. Place in refrigerator for at least 1 hour to set.
Store in the refrigerator in an airtight container. Makes about 36 bonbons.