It can be difficult to make healthier items taste as good as more traditional items. I find that the best way to accomplish this seemingly daunting task is to simply "amp-up" the ingredients.
When I make bran muffins, I know that the wheat bran is nearly flavourless and can handle more pungent flavours. Traditionally, muffins rely heavily on the fat and sugar to carry the flavours. However, as you probably know, these two things are usually what you're trying to reduce when transitioning to healthier options. So here are my suggestions:
If you are replacing fat with a neutral oil or applesauce, increase your salt. Even if you add two pinches instead of one, this will make a huge difference.
Greek yogurt is a great ingredient to incorporate for a moist and rich muffin.
Use fresh ingredients! It seems obvious but by using a fresh lemon instead of bottled lemon, your baked goods will come out far more tasty.
Zest, zest, zest. Adding fresh zest from a lemon, orange, or lime makes a world of difference. There is so much flavour jam packed into that thin rind...take advantage of it!
Add freshly grated ginger. If you don't want the taste of ginger, only add about a teaspoon. This addition adds a freshness and works with the zest to amply the flavours you've incorporated.
My final tip, freeze bran muffins the day of as soon as they are cooled. Wheat bran dries out very quickly so unless you're confident that all of the muffins will be consumed in a matter of a few hours, freeze until you're ready to enjoy!