Yes, Chapter III begins in the Bulldog. There is excellent symmetry between the end of Chapter I (driving away in the hunters' Rover after a fight) and the current situation (driving away in the runners' Bulldog after a fight). Rednblack, intentionally or coincidentally, mirrorered Poindexter's last post from Chapter I.
Doc doesn't necessarily need to wait 8 more minutes to shake off the last effects of his Disorientation from dumpshock, but he'll still be at a -2 modifier until he does so.
A destination would be an important decision, especially given the condition of the Bulldog's tires. Final decision is 8-bit's, since Chino is driving. Options include:
Woody Creek: 5 miles / 8 kilometers, Population 250
Snowmass: 12 miles / 19 kilometers, Population 250
Basalt: 16 miles / 26 kilometers, Population 4,000
Carbondale: 27 miles / 44 kilometers, Population 6,500
Defiance (a.k.a. Glenwood Springs): 39 miles / 63 kilometers, Population 10,000
As previously stated, the tires will only last about 50 kilometers unless you lighten the load (or get new tires).