It's been 4 days since the exterminator dusted the entrance, and we are still getting the occasional bee in the house.

2 days. The product kills by dehydration. Your use of entrance can mean "bee entrance" or "house entrance" or "entrance to bee's nest".

Usually the nest is found, dusted and sealed. If an entry point is found, then the bee has to go through it and bring it to the nest.

Assuming you mean the entrance to the nest and that the nest was in the walls of your house, you may continue to get a "straggler" up to 10 days after treatment. These will be bees that were ready to hatch when it was treated.

If you continue to see bees after 10 days, there may be a secondary nesting site which will also require treating.

If my assumptions were off, please correct them so I can advise further.