Joining the Jumu`ah Prayer During Tashahhud
Question

If someone reaches Jumu`ah during the Tashahhud, what should he do? If someone is held up by something out of his control eg. bus breaks down... is he sinful if he is late to Jumu`ah or misses it? Does he miss out on the rewards he would have gotten and the moment of the acceptance of Du`a, etc.?
Praise be to Allah.How to catch up with Friday prayer
You can only catch up with the Jumu`ah prayer if you catch a Rak`ah with the Imam, and catching a Rak`ah means catching up with the Ruku` with the Imam.
If you catch up with the Imam before he stands up from Ruku` in the second Rak`ah, then you have caught up with the prayer, and you should then complete your prayer after the Imam says the Salam. You should stand up and complete the remaining Rak`ah of your prayer. 
However, if you catch up with the Imam after he has stood up from Ruku`, this means that you have missed the Jumu`ah prayer, and have not caught up with it. In this case you have to pray it as Zuhr. You should stand up after the Imam has said the Salam and complete your prayer with four Rak`ahs, because it is Zuhr and not Jumu`ah. 
This is the view of the majority of scholars, Malik, Al-Shafi`i and Ahmad (may Allah have mercy on them). (See Al-Majmu’ by Al-Nawawi, 4/558)
They quoted several texts as evidence, such as: 

The words of the Prophet (peace and blessings of Allah be upon him): “Whoever catches up with one Rak`ah of the prayer has caught up with the prayer.” (Al-Bukhari, 580; Muslim, 607). 
The report narrated by Al-Nasa’i from ‘Abdullah ibn ‘Umar (may Allah be pleased with him), who said: “The Messenger of Allah (peace and blessings of Allah be upon him) said: ‘Whoever catches up with one Rak`ah of Jumu`ah or any other prayer, let him add more Rak`ahs to it to complete his prayer.’” (Classed as authentic by Al-Albani in Al-Irwa’, 622). 

Missing the prayer for a valid excuse
If a person does not catch up with the prayer for a reason that is beyond his control, such as the bus breaking down, as mentioned in the question, or other excuses such as oversleeping or forgetting, then there is no sin on him in that case, because Allah says (interpretation of the meaning): 
“And there is no sin on you concerning that in which you made a mistake, except in regard to what your hearts deliberately intend” [Al-Ahzab 33:5]
A person in such cases does not deliberately intend to miss the prayer . 
The Prophet (peace and blessings of Allah be upon him) said: “Allah has forgiven my Ummah for what they forget and what they do by mistake, and for what they are forced to do.” (Narrated by Ibn Majah; classed as authentic by Al-Albani in Al-Irwa’, 82) 
In this case, if one is sincere in his resolve to pray, but has an excuse, he will earn the reward in full, because the Prophet (peace and blessings of Allah be upon him) said: “Actions are (recompensed) by intentions, and every person will have but that which he intended.” (Al-Bukhari, 1; Muslim, 1907) 
The Prophet (peace and blessings of Allah be upon him) also said to his companions on the way back from the battle of Tabuk: “In Madinah there are men who, whenever you cover a distance or cross a valley, they share the reward with you; they have been detained by sickness.” (Muslim, 1911)
And Allah knows best.