Praise be to Allah, and peace and blessings be upon the Messenger of Allah. To proceed:
Yes, a person is held accountable for the action he chooses and through which he causes harm. This does not contradict the fact that the accident and death occur by the decree and predestination of Allah.
If someone rides a bicycle at excessive speed or in a reckless manner and thereby causes the death of another person, he is sinful because of his transgression and negligence. He is also required to fulfill what Islamic law prescribes for accidental killing, namely blood money (diyah) and expiation (kaffarah), and he must repent if he was negligent.
The evidence is the saying of Allah, the Exalted: ﴿It is not for a believer to kill a believer except by mistake﴾ [An-Nisa’: 92].
It is not correct for him to say, “His death was decreed, so I bear no blame,” because divine decree cannot be used as an excuse for sin and negligence. Allah, the Exalted, decreed the death, and He also decreed its cause. He has given human beings ability and choice, and therefore holds them accountable for what they do by their own choice.
A person is therefore not held accountable for the prior decree of Allah itself. Rather, he is held accountable for the action he chose and was capable of leaving undone.
Nevertheless, when such an incident occurs without the intention to kill, it does not have the ruling of intentional killing. Rather, it falls under accidental killing, which has its own Islamic legal rulings.
In conclusion: The fact that death is decreed does not remove the responsibility of the person who caused it. Death occurs by Allah’s decree, while negligence and excessive speed are actions that a person chooses, and therefore he is held accountable for them.
And Allah knows best.