To paraphrase Mark Twain, everybody talks about the Mint Julep but nobody ever does anything about it.
I recently read some magazine article - can't remember where now - that talked about how played-out, overrated, and overhyped the Mint Julep is. They talked to some bartender who said she rarely is ever called upon to make one, except by the occasional rube tourist at Derby time. The article also stated that although people go through the motions of having Mint Juleps for Derby, few people actually like them and they toss them aside after a few token sips for tradition's sake.
I posit that the reason these people feel this way about the Mint Julep is because they've never actually had one prepared properly. Hint: it doesn't come from a pre-made bottle, it doesn't come from a store-bought syrup, and it doesn't come from a mix. That this goes without saying should go without saying.
If you really want to do it right, follow the poetic instructions of General Simon Bolivar Buckner Jr. to the absolute letter. Failing that, here's my simple solution that doesn't involve simple syrup:
Fresh mint leaves
Finely crushed ice
Muddle one pinch of mint with the granulated sugar in a metal Julep cup. Some will tell you to just gently bruise it and not pulverize it, but I say go nuts and pound the hell out of it. The granulated sugar will help give you something to grind against.
Fill the cup to the top with finely crushed ice, fine as a Sno-Cone. Pour bourbon almost to the top, then add your second pinch of mint. It's your second pinch, that will garnish the top, that you want to just mildly bruise and not smush into pieces. Then dust the top generously with powdered sugar.
Those with bourbon-sensitive palates should note that a proper Julep, contrary to how it's commonly fixed, is essentially bourbon with a little mint and a little sugar, NOT mint and sugar with a little bourbon. If you prefer bourbon-based drinks in which you can't taste the bourbon, you might consider the likelihood that bourbon-based drinks are not for you.
Also note that a metal cup is a must - preferably a genuine Julep Cup intended for this purpose, and if it's an antique one (see image of mine above), all the better. If you're doing it in a container made of glass or plastic, don't even bother. Just have a Gin Rickey instead or something.
Alternate versions: if you're dead set on having a Mint Julep even though you don't like bourbon, may I recommend cutting the bourbon somewhat with either Barenjager (my first choice) or Southern Comfort. I suppose eliminating the bourbon entirely in favor of these beverages is permissible - what the hell, it's your drink, buddy - but the thought of it makes the purist in me all fremdschämen.