Bridge Mt is a very prominent skyline feature in the Red Rocks National Conservation Area, a mere 17 miles from the Las Vegas Strip. While Red Rocks is one of the most popular climbing areas in the US, this not commonly climbed because it's not technical enough for climbers and too technical for hikers. Thus, it's one of the ten best summits in North America for the intrepid.
Other route descriptions spend time describing how to drive up the approach road - don't do that - the FKT route starts at the exact edge of the pavement down in the parking lot, goes up the 4WD road (easier to run than drive), to the saddle and a trailhead sign. Follow the trail up to a ridge where the view explodes and the fun begins. Descend significantly into the red slickrock, and marvel at the intimidating route up ahead - "You will swear it is 5.8, but remarkably it is only 3rd class." - Mountain Project. It's actually serious 4th class, but is on beautiful high quality rock. The route to the summit is amazingly complex from there, going past the namesake and spectacular bridge, a huge tinaja (pothole), a hidden Ponderosa Pine forest, and more exposed scrambling, including short descents while ascending.
Las Vegas is plainly visible in the distance. Don't try this in summer, when it's wet, or if you're not comfortable with exposure while on rock.