The incident happened at the bottom of The Hough on Thursday, March 28.
Police have sealed the road off at Stump Cross.
First Bus confirmed at about 7.30am that there will be diversions on the 508 service.
It will be diverting via Queensbury Road and Denholme Gate Road both ways until the lorry is cleared.
The 548 will also divert via Queensbury. The 549 service will divert via Southowram both ways.