Praise be to Allah.
You can only catch up with Jumu’ah prayer if you catch with a rak’ah with the imam, and catching up with a rak’ah means catching up with the rakoo’ with the imam. If you catch up with the imam before he stands up from rukoo’ 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 salaam, so you should stand up and complete the remaining rak’ah of your prayer. But if you catch up with the imam after he has stood up from rukoo’, this means that you have missed Jumu’ah prayer, and have not caught up with it. In this case you have to pray it as Zuhr, so you should stand up after the Imam has said the salaam 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, Maalik, al-Shafaa’i and Ahmad (may Allaah have mercy on them). (See al-Majmoo’ by al-Nawawi, 4/558). They quoted several texts as evidence, such as:
1 – The words of the Prophet (peace and blessings of Allaah be upon him): “Whoever catches up with one rak’ah of the prayer has caught up with the prayer.” (al-Bukhaari, 580; Muslim, 607).
2 – The report narrated by al-Nasaa’i from ‘Abd-Allaah ibn ‘Umar (may Allaah be pleased with them both), who said: “The Messenger of Allaah (peace and blessings of Allaah 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 saheeh by al-Albaani in al-Irwa’, 622).
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 falling asleep or forgetting, then there is no sin on him in that case, because Allaah 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-Ahzaab 33:5]
A person in this case does not deliberately intend to miss the prayer.
And the Prophet (peace and blessings of Allaah be upon him) said: “Allaah 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 Maajah; classed as saheeh by al-Albaani in al-Irwa’, 82).
In this case, you were sincere in your resolve to pray, but you had an excuse, so you will earn the reward in full, because the Prophet (peace and blessings of Allaah be upon him) said: “Actions are but by intentions, and every person will have but that which he intended.” (al-Bukhaari, 1; Muslim, 1907).
And the Prophet (peace and blessings of Allaah be upon him) said to his companions on the way back from the campaign of Tabook: “In Madeenah 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 Allaah knows best.