Despite what some traditionalist might preach, there is no singular correct way to eat bibimbap. For us, the fried egg and the Korean chilli sauce is our favorite part. So much so that I like to eat Bibim Bop with two fried eggs.  I put the fried egg to the side, add the Korean chilli sauce to taste and mix everything thoroughly in the bowl,, and then put the egg back on top. I enjoy having a piece of fried egg in each bite for the contrast it provides from the rest of the ingredients. 

More helpful tips to enhance your Bibimbap experience:

• Mix thoroughly. Vegetables tend to clump up so mix everything evenly. 
• Add the sauce in increments. Everyone prefers a different spice level so its best to add sauce in small amounts while mixing. The sauce should be the glue that enhances the flavor of all the ingredients, not overwhelm them.
• Put your favorite ingredient to the side. You can keep an element like the beef bulgogi  on the side and mix everything else. With this method you can taste the bulgogi on its own and it's like having two dishes in one. Bulgogi and vegetable bibimbap.
• Leftovers are good. We have found that bibimbap makes for a great leftover dish. Stir fry the leftovers in a non-stick pan at high heat with some vegetable/canola oil till it gets a slight char. This technique produces a flavor similar to Dol Sot (stone pot) Bibimbap.