Chewing gum is cheap, I get that. So why make it yourself? I get that, too. But think of all the possibilities that come with creating your own flavors: lemongrass, basil, lemon, and yes, bitters. Even reducing port or cocktails down to a syrup could be full-on cocktail flavored gum: This is just the base, the ideas are endless.
Start with 60g of corn syrup and soften to a more liquid form in the microwave for about 20-30 seconds. As soon as that becomes the correct texture, start melting your 60g of gum base in timed increments, stirring each round until malleable and fully melted. Use a microwavable container that you can throw away afterward, because getting this stuff out of a glass bowl takes longer than the whole making the gum process. Trust.
Incorporate the corn syrup in to the gum base and stir thoroughly, then add the flavoring of your choice. Take 75g grams of confectioners sugar and use as sort of a bench flour. Knead your gum until there are no sticky parts left — you may have to stretch it out, refold, and knead a couple times to fully incorporate.
Discard the remaining confectioners sugar and roll the gum in to a long snake, just like you did with Play-Doh when you were a kid. Take a knife and cut the long tube into one-inch pieces. Wrap in pieces of wax paper and put on your desk for others to enjoy (or judge you, whichever).