This is an easy Class 1 hike (with hiking poles). (Viz. NO need to bushwhack!!)
After passing through the Bulldog Canyon gate, as the main road veers left, take the signed 1356 dirt road to the right. When 1356 makes a 90-degree turn to the right (east) at what looks like a "roundabout", take the dirt road to the left (NW).
After about 1/4 mile, take the road that turns off to the right (north).
Take this road north to its highest point (~2350 ft). As the road descends, you will see the trail turn off to the right (north). (If you go to the end of the road [all downhill], you've gone too far).
This trail is marked by 2 cairns a few feet apart, one roadside cairn and some dead saguaro cactus "sticks" stuck in the ground. THIS TURN OFF IS THE CRUX OF THE ROUTE.
Take this defined hiking trail to the summit of Dome Mountain. After the trail turns left at the saddle between Dome & Peak 3134, you will see frequent white spray-paint stripes on the trail all the way to the summit.