The pedestrian, who police said was in his 30s, fell from the bridge shortly after 5pm on Saturday January 15.
The man was pronounced dead by paramedics a short time later. Officers said the man's next of kin have been informed.
The road was closed in both directions for several hours and did not reopen until after 1am on Sunday January 16.
North Yorkshire Police are now appealing for anyone who may have information or who witnessed the "extremely upsetting" incident, to come forward.
Officers said that many people who were in the area at the time have already come forward, but that the full circumstances surrounding the man's death need to be investigated.
They are urging anyone who was travelling in the area just before 5pm until around 5.10pm to get in touch.
Officers are particularly keen to speak with anyone who has dashcam video fitted in their vehicle and any residents or businesses along the B1248 who have CCTV or a video doorbell.
A North Yorkshire Police spokesperson said: "As you can imagine this has been an extremely upsetting incident for all involved and our thoughts are with the man’s family at this time.
"We also know the impact an incident of this nature can have on those who witnessed it or assisted in the aftermath.
"We would strongly encourage those people to speak with someone, and if needed, to seek advice from a professional – there are a list of agencies who may be able to help on our website.
"If you are able to help officers with their investigation, please provide reference NYP-15012022-0367 when providing information."