What is the truth about the bridge over hell in the Day of Judgment?

Allah tells us in the Qur'an that every single person shall come close to hell. He says:
"Every one of you will come within sight of it: this is with your Lord a decree that must be fulfilled. We shall then save [from hell] those who have been God-fearing: but We shall leave in it the evildoers, on their knees." [Mary — “Marium” 19: 71-72].

There are several Hadiths which mention "the bridge to hell". While one-report mentions that this bridge is as sharp as the edge of a sword, the more authentic ones do not mention that particular aspect. These authentic Hadiths mention that believers will cross it as quickly as a wink, or lighting, or wind, or fast horses. What determines their speed is the quality of their deeds in this world. Those with the best deeds are the first and the fastest to cross it. In a Hadith reported by Abdullah ibn Massoud, the Prophet, peace be upon him, is quoted as saying: "They [i.e. believers] are told to save themselves according to their light [which is given them in proportion to their good deeds]. Some of them will pass as quickly as a wink, some as wind, some as birds, some as fast horses and some like the people running. The last of them is a man who has no more light than the size of his large toes, and who stumbles over the bridge. In one version of this Hadith, this last person is reported to turn to Allah and ask Him why has He made his crossing so slow. Allah will answer him: "It is your deeds that have made you slow."