Having completed my trip I wanted to report that GoGo Bus provided very good service and I appreciated their use of comfortable 6 passenger vans rather than buses. The system at HKIA is also user friendly. They give you a sticker with your destination written in Chinese. You wear it on your clothing so you won't get lost at the transfer point.

You do have to change vans at the border, which is the only place where their timetable can get messed up. In light traffic it's about 45 minutes from HKIA to the land border near Shenzhen. It's another 45-60 minutes to Dongguan, depending where in the city you are headed. However you'll probably have to cool your heels at the border for 45 minutes or longer while your driver waits in a slow moving line of cars, all clearing customs and immigration. I saw no intrusive inspections and the actual border formalities are short but the process takes a while because most of the cars have multiple passengers and everyone's documents have to be inspected at least twice.

I would have preferred to take the ferry, which can be done from HKIA without entering Hong Kong, but my flight arrived after the day's last ferry had departed for Dongguan.
I recommend GoGo bus however, and they deliver you to the door of your hotel.