If you don’t want to do the full round it is possible to do a shuttle from the Buck Creek Bridge up B1000 and B1300 until it dead-ends. You are then a mile from the Monte Carlo summit. The climb still involves about 300 yd of hike-a-bike, but is mostly ridable. It is also worthwhile doing a 1.5 mile out-and-back along the Monte Carlo ridge to a really good view point at a rocky outcrop.

Myself and Phil Jones attempted to ride this in August 2009.
(using the square numbers from the above pdf map as reference).
1. To avoid most of the road climb, start from the parking at 27.
2. Climb the green trail to Nester Peak. (Brutal climb)
3. Take green trail to junction of N1000, N1700 at lower right of 19.
4. Stare at trail sign across road pointing into virgin bush. The section to where it reconnects with B1000 at the top left of 18 either never existed or has completely reverted.
5. Green trail to Buck Creek Trailhead 2 exists but is very heavily overgrown with lots of blow down.
6. Where the trail goes from, the inappropriately named, Trailhead 2 is a mystery – there is no evidence of any outbound trail.
7. We descended B1000 and then climbed back to the trail using B1300 in section 15 (brutal climb).
8. There is a trail coming from top left of 15, but how this connects to Trailhead 2 is unknown.
9. The descent back to the parking used to be a great downhill (as of 2004), but is now badly degraded
with many rocks fallen on the trail.

At best option as of now is to climb Nester Peak and the return down the same route.