The pavement drive part (well, most of it is paved) from 395 & 9 MCR to the Blackrock Ranger Station is only ~45 minutes, if you know the road. Give yourself an hour or more because they are a few surprise turns to scare you a mile or two after you enter the Forest (if it's ran too fast).
The dirt part of the Monache Jeep trail is north of Blackrock, off the highway down a side road. Without experience driving the trail it takes about an hour to get to Monache Meadow, and another 15 minutes to Bakeoven or to the trail end at the Kern near the Golden Trout Wilderness boundary.
The trail is not too difficult (most years it can be driven in a long wheelbase 2WD), but it does see winter impacts and water in meadows and crossings (making it more difficult early in the season).
Call the Blackrock Ranger station to ask if the trail is open. There are gates, and it is closed seasonally to prevent watershed damage around some of the smaller meadows. They usually open before Memorial Day, depending on the mud.
www.topozone.com can show a map if you enter "Monache", as it's the quad for the area of the meadow. The surrounding quad maps can be linked.