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The first clue about the accuracy of the statement is the use of the word "bees". While the word tends to make us think of honeybees, they are only one of about 20,000 different species of bee. Some of species of bee are endangered, but the honeybee is not. In spite of colony collapse, pesticides, etc., there are more managed beehives now than there have been in the past 20 years, and the number is increasing. Honeybees are not in danger of disappearing.
Studies have shown that compared to native bees, honeybees do a relatively poor job of pollination. Then why so much focus on the honeybee? Because honeybees tolerate the movement of their hives, allowing us to move them from field to field, area to area. This makes large scale, single crop farming work possible. If all of the plants in a huge area are all one species, they all flower at the same time. That means a huge demand for pollinators (honeybees) for a short time, and large part of the year with no flowers at all for native pollinators. If honeybees did somehow vanish, it would mean an end to the giant, factory farms, but smaller, more diverse farms would still have plenty of native pollinators to get the job done.