fastest mode of transportation from zhuhai to shenzhen and guangzhou

No bullet train connects Shenzhen. Well, the fastest way is ferry. You can easily take one at local Jiuzhou Port to Shenzhen Shekou Port in an hour.

To Guangzhou, bullet train is the best way indeed. It takes 70-80min to arrive at Guangzhou South Station.

To have a connecting trip, I suggest you take a bullet train to Guangzhou first. After touring, board the intercity bullet train to Shenzhen for a visit. U will arrive at Shenzhen North. Then it is fine to walk to the nearby North Bus Station to take a direct bus to return. Or take a taxi to Shekou Port to catch a ferry instead.