I know that there is a ferry from Saigon (Hồ Chí Minh City District 1 downtown) to Thủ Thiêm across the Sông Sài Gòn (Saigon River), but I don't believe there is a water bus or taxi system to take people up or down the river. There is a hydrofoil boat service between Vũng Tào on the coast and Saigon.
Bangkok offers a good mass-transit model for HCMC with its Chao Phraya River Express water buses. These long boats run up and down the Chao Phraya River, stopping at piers numbered like bus stops. The fare is collected on board and amounts to only US 40 cents or less depending upon the distance to be travelled.
Other long-tail boats ferry passengers up and down the numerous khlongs or canals intersecting through the city.
The Sài Gòn River winds through Thành Phố Hồ Chí Minh very similarly to the river in Bangkok. There are also several canals through the city that could support water taxi service after the City completes its environmental clean-up of the black water.
In Bangkok, the water buses are large and roomy to allow standing when necessary by commuters during the rush hours.
The pier stops are located at strategic points allowing access to tourist and business centers.
Some of the stops are located on the Thonburi side of the river from central Bangkok, supplementing the cross-river ferries.