How Will People Pass Over the Sirat?
Question

Is it true that passing over the Sirat will take one thousand years for the ascent and one thousand years for the descent?
Praise be to Allah.The Sirat is a bridge that will be set up over Hell – may Allah protect us from it – over which people will pass according to their deeds. Some will pass as fast as the blink of an eye, or as fast as lightning, or as fast as the wind, or as fast as swift horses.
Some will cross running, some walking, some crawling, and some will be snatched and thrown into the Fire, each according to his deeds.
In Sahih Al-Bukhari (7439) and Muslim (183) it is narrated from Abu Sa`id Al-Khudri (may Allah be pleased with him) in a lengthy Hadith: “……Then the Sirat will be laid across Hell.’ We said, "O Messenger of Allah! What is the Sirat?’ He said, ‘It is a slippery bridge on which there are clamps and (hooks-like) thorns which are wide at one side and narrow at the other and have bent ends. A plant with such thorns is found in Najd and is called Al-Sa`dan. Some of the believers will cross the bridge as quickly as the wink of an eye, some others as quick as lightning, a strong wind, or fast horses or she-camels. So some will be safe without any harm; some will be safe after receiving some scratches, and some will fall down into Hell (Fire). The last person will cross by being dragged (over the bridge).”
Muslim added: Abu Sa`id (may Allah be pleased with him) said: “I heard that the Sirat is narrower than a hair and sharper than a sword.”
An-Nawawi (may Allah have mercy on him) said:
“The words “So some will be safe without any harm…” mean that they will fall into three categories: one category will be safe without experiencing any harm at all; another category will be scratched, then released and will be saved; and a third category will be snatched and thrown and will fall into Hell ." (Sharh An-Nawawi ‘ala Muslim 3/29)
Shaykh Ibn ‘Uthaymin (may Allah have mercy on him) said:
"The Sirat is a bridge that will be set up over Hell; it is narrower than a hair and sharper than a sword. People will pass over it according to their deeds. Whoever used to hasten to do good deeds in this world will pass quickly over the Sirat; whoever was slow to do good deeds and whoever used to mix righteous deeds with bad deeds, and his bad deeds were not forgiven by Allah, may slip into the Fire; may Allah protect us.
People will vary in the ways in which they pass over the Sirat. Some will pass in the blink of an eye, some will pass as fast as lightning, some will pass as fast as the wind, some will pass as fast as swift horses, some will pass as fast as fast camels, some will walk, some will crawl, and some will be thrown into Hell. No one will pass over this Sirat except the believers only. As for the disbelievers , they will not pass over it, because on the Day of Resurrection they will be driven directly to Hell." (Sharh Riyadh As-Salihin 1/470)
This is a summary of what has been narrated concerning the passing of the people over the Sirat, which will vary according to their deeds.
Whoever used to hasten in this world to obey and worship Allah will be quickest in passing over the Sirat.
Whoever was slow (to obey and worship Allah) will pass over it slowly. 
With regard to what is mentioned in the question about passing over it taking one thousand years to ascend and one thousand years to descend, we do not know of any basis for that. What one must do is stick to the texts and what they indicate.
For more details, please see the following answers: 22467 , 21672 , 43840 , and 78329 .
And Allah knows best.