Bugambilias isn't the sort of place you'd just wander into, not unless you live in the vicinity of Lancaster Road between Orange Avenue and South Orange Blossom Trail. If you do live in the area, you know there are myriad Mexican restaurants, many as authentic as you're likely to find in the area, to choose from. Bugambilas would be a good choice.
Though it isn't a guarantee of authenticity, it's a pretty good indication of it when one has to ask if a menu is available in English. (One was.)
While I was still trying to navigate through the Spanish version, I was drawn to the Pozole, a favorite of mine. But when I failed to notice it was available only on Saturdays and Sundays, I figured I'd better switch to my first language. (Not that there's a second one, mind you.)
Instead I chose the Birria, shown at top, which is available todos los dias. Birria is basically a beef stew and is a traditional dish from the Jalisco region, which is home to Guadalajara. This isn't a stew like American versions -- there are no carrots or potatoes or peas. But on the other hand, it isn't made with goat or mutton, as it might be in Mexico.