I want to fly at 77° 38' and 38° 56'. This is in the DC SFRA, in class B airspace (starting at 1500ft MSL). Can I fly here as a part 107 pilot without asking permission?
Flight by sUAS in the outer ring of the DC SFRA is permitted, and is discussed in the FAA website: https://www.faa.gov/uas/where_to_fly/no_drone_zone/
It's off topic, but I believe that there are some errors on that web page.
You may still have to ask for permission within the outer ring, depending upon other parameters of your flight.
It is noteworthy that 101 operations may not be permitted. https://www.faa.gov/documentLibrary/media/Advisory_Circular/AC_91-57A_Ch_1.pdf near the end of the chapter.
There are two questions here. The first question is in the thread title. The second question is in the OP. But they are two different questions. It's possible the OP was edited after it was initially posted and after several answers were given.
The correct answer to the first question is yes provided the flight takes place outside the DC FRZ.
The correct answer to the second question is no because you state you are flying in Class B airspace. Ironically it has little to do with flying in the outer ring of the DC SFRA which would otherwise be permitted.
You say you are flying in Class B. Flying in Class B requires authorization via the FAA's dronezone portal linked here: https://www.faa.gov/uas/request_waiver/
You may fly in Class B (or any controlled airspace) only after your online request for waiver or authorization is approved by FAA.
Don't confuse this with a Part 101 flight which has different rules.
I am posting this for anybody who might be looking for this info in a search.