How many nesting pairs of bald eagles are estimated to be alive today?

About 50,000 in Alaska alone. Probably another 40,000 in Canada. Maybe another 10,000 in the lower 48 states.
In 2007, it was estimated that in the lower 48 states (excluding Alaska and Hawaii) there were 10,000 nesting pairs. That would be about 20,000 bald eagles.

The bald eagle population was estimated to be nearly 50,000 in Alaska alone in 2000, and with a doubling of the population every seven years, there has to be at least 200,000 in the US today.

Source: IUCN Redlist, Species of least concern.